Manufacture of display devices with ultrathin lens arrays for viewing interlaced images

ABSTRACT

An assembly for fabricating a device for displaying an interlaced image. The method includes providing a film of transparent material and creating a lens array in the film by forming parallel lens sets on a first side of the film, and then bonding an interlaced image including sets of elongate image elements to a second side of the film. Each of the lens sets is configured with lenses for focusing light from one of the image elements in a particular paired set of image elements rather than all the elements as with lenticular material. The bonding of the interlaced image to the film may include printing the interlaced image directly onto the second side with the printing facilitated by the small lens array thickness. Lens array creating includes embossing the lens sets into the film with a flat die or cylinder/roller engraved with a reverse image of the lens array.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to co-pending U.S. application Ser. No.11/558,523, filed Nov. 10, 2006, and entitled Ultrathin Lens Arrays forViewing Interlaced Images, which is incorporated herein by reference inits entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates, in general, to lens arrays and devicesfor use in viewing or displaying images that are interlaced to displayanimated, three-dimensional (3D), and other images, and, moreparticularly, to very thin lens arrays, as well as productsincorporating such lens arrays and methods of fabricating such lensarrays, that include numerous, repeating sets of lenses or lensmicrostructures that are specially configured for viewing an interlacedimage by pairing each lens in the set or microstructure with only one of(or a smaller subset of) the interlaced image elements or slices.

2. Relevant Background

Elaborate graphics can be produced with lenticular graphic labels toprovide three-dimensional (3D) and animated imagery such as a short clipof a movie. For example, lenticular lens material is used in thepackaging industry for creating promotional material with appealinggraphics and typically involves producing a sheet of lenticular lensmaterial and adhesively attaching the lenticular lens material to aseparately produced object for display. The production of lenticularlenses is well known and described in detail in a number of U.S.patents, including U.S. Pat. No. 5,967,032 to Bravenec et al. and U.S.Pat. No. 6,781,761 to Raymond.

In general, the production process includes selecting segments fromvisual images to create a desired visual effect, slicing each segmentinto a predefined number of slices or elements (such as 10 to 30 or moreslices per segment), and interlacing the segments and their slices(i.e., planning the layout of the numerous images). Lenticular lenses orlens sheets are then mapped to the interlaced or planned segments, andthe lenticular lenses are fabricated according to this mapping. Thelenticular lenses generally include a transparent web that has a flatside or layer and a side with optical ridges and grooves formed bylinear or elongated lenticules (i.e., lenses) arranged side-by-side withthe lenticules or optical ridges extending parallel to each other overthe length of the transparent web. To provide the unique visual effects,ink (e.g., four color ink) is applied to or printed directly on the flatside of the transparent web to form a thin ink layer, which is thenviewable through the transparent web of optical ridges.

Each lenticule or lens of the lenticular layer is paired or mapped to afairly large set or number of the interlaced image slices or elements.For example, one lenticule may be paired with 10 to 30 or moreinterlaced image slices or elements associated with the image segments,and generally only one of the slices is visible through the lenticule ata time based on the position of the lenticule relative to a viewer'seye. In other words, the animation, 3D, or other graphic effect isachieved by moving the lenticule or the viewer's position tosequentially view each of the interlaced image slices under thelenticule and allow a viewer to see each segment of the image bycombining the slices viewed from all the lenticules.

In producing conventional lenticular lens material, it is desirable touse as little material as possible, i.e., to produce effectivelenticules or lenticular lens arrays with as thin as web material aspossible. Decreasing lens thickness is also desirable such to facilitatefabrication using techniques such as web printing that are verydifficult or impractical with thicker lens materials. Thin lenticularlens material is desired to save on material costs and to provide arelatively flexible lens material or substrate that can be easilyapplied to products and product containers, such as in a label that canbe attached to a box or to a bottle as part of a wraparound label or ona cup to provide desirable visual effects. To make lenticular lensmaterials thinner, the whole structure must be properly scaled downwardtogether. In other words, the lenticules and the printed interlacedimage must be shrunk or made smaller together to allow proper mapping ofthe image slices to the lenticules.

However, such shrinking of the lenticules has proven very difficult withlimitations associated with printing the interlaced images oftenpreventing the lens layer or web being made very thin. As noted above,all the interlaced slices for each segment are placed underneath asingle lenticule such that numerous slices have to be printed with verylittle width to be mapped to the lenticules width or pitch. However, theprinting can presently only be done with a limited degree of resolution,and this forces the lenticular lens material due to printingpracticalities and resolution to be provided in coarser frequenciesranging from about 10 lenticules per inch (LPI) to about 200 LPI. Withcoarser lens arrays (i.e., with lower the frequency or LPI), theprinting can be accomplished more easily and mapping to lenticules ofthe image slices achieved more accurately. However, coarser lens arrayswith frequencies of 10 to 30 LPI tend to be very thick because generalphysics or optical rules for focusing with conventional lenticularmaterial require that more lens thickness or more lens material beprovided to achieve effective focusing. For example, a 15 LPI lenticularlens array with a fairly common viewing angle (such as a 22-degreeviewing angle) may be mapped to an interlaced image that printed orprovided directly behind the lenticular lens array, with each of thelenticules in the lens array being mapped to or paired with all imageslices of a paired segment of the interlaced image. If the lens array isformed from acrylic, the lens array would need to be about ⅜-inch thickto enable the lenticules to properly focus on the paired image slices.Conversely, the frequency of the lenticular lens array may be increased(i.e., a finer lens array may be used). However, existing limitations onprinting have resulted in the thinnest lenticular lens arrays being atleast about 15 to 30 mils thick, and the mapping accuracy required atthese lower thicknesses and high lenticule frequencies often results inlower quality imaging results and increased fabrication or printingcosts.

There remains a need for a lens array or structure that provides analternative to conventional lenticular lens arrays such that lens arraysor structures can be provided with less thickness and with enhancedmapping of interlaced image slices or elements to the lens array forimproved visual effects. Preferably, such a new lens array would be easyand inexpensive to fabricate, would be well suited for fabrication withthicknesses less than presently achievable with lenticular lensmaterials (e.g., less than about 15 to 20 mils), and would still beuseful for providing desired viewing angles (e.g., 20 to 40 degreeviewing angles or the like) to view conventional interlaced images(e.g., images interlaced as for use with conventional lenticularmaterial to achieve 3D, animation, or other visual effects).

SUMMARY OF THE INVENTION

The present invention addresses the above problems by providing ways tomanufacture lens substrates or arrays formed with numerous lensmicrostructures or lens sets. Each of these lens microstructures can beused to provide the functionality of a much thicker lenticule or lens ofconventional lenticular material as each of the lens microstructures ispaired to a set of interlaced image elements or slices, which may beprinted digitally, printed with offset printing, printed using webprinting, or the like. The lenses of the lens microstructure are eachused to focus onto or from a small subset of the slices in a paired setrather than focusing on all of the slices of the set as is required of alenticule in conventional lenticular technology. Further, the lenses ofthe lens set or microstructure are each uniquely configured (e.g., witha differing cross sectional shape) to provide its own main viewingdirection or focus line/direction such that each lens in a lensmicrostructure displays the small subset of images (e.g., 1 to 3 images)to which it is mapped and with a lens-specific viewing angle or angulardistribution. In practice, the lens microstructures have an overallviewing angle that is generally the combination of the angulardistribution of each lens of the lens microstructure with the focuslines or directions of each lens selected such that only select ones ofthe image elements or slices are displayed or visible as a viewer's lineof sight moves through the overall viewing angle. The lens arrays may besignificantly thinner than possible or practical with conventionlenticular material (e.g., 50 to 90 percent or more reduction in lensthickness), which allows the “paper thin” arrays to be applied to orprovided integrally in numerous product surfaces such as in printedlabels, attached decals or labels, book jackets, magazine coverswraparound labels, and many other print and packaging applications.

An ongoing problem with traditional lenticular lens material used tofocus on and magnify printed interlaced images is that the lens arraysor material had to be relatively thick to be effective. Lenticulararrays need to be manufactured to follow optical laws or laws of physicssuch as Snell's Law such that the focus of these lenticules isdetermined by the radius of the lens and index of refraction of thelenticular material combined with other parameters including frequencyand array thickness. A general problem with lenticular arrays is that inorder to decrease the thickness of the lens or associated arraythickness to lower costs and to enhance its application (e.g., thickplastic lens material does not process well, is difficult or impossibleto bend, and is hard to wrap on curved surfaces), the frequency of thelenticules in the array must be increased (e.g., the lenticules per inchor LPI must be increased). As the frequency is increased, the thicknessof the lens or lens array may be decreased, but, unfortunately, thequality of the displayed image or visual effect generally alsodecreases. More specifically, as the lenticule frequency is increasedand the thickness is decreased, the ability to print high qualityinterlaced images to produce 3D and animation becomes exponentially moredifficult because the slices or image elements have to be provided atvery fine widths, i.e., at high frequencies. For example, if it weredesired to use a 12-mil thick lenticular lens array, the lenticuleswould have to be provided at a very high frequency (such as about 167LPI) to produce a quality display and the image elements may need toprovide sets of twelve images under each lenticule. As can beappreciated, printing an interlaced image for such a lens array becomesquite difficult and cannot be done with some printing techniques such asroll form as the image elements have widths of 0.000139 inches (1/167-inch divided by 12), which is impractical for most printingapplications particularly a CMYK format in which all colors mustregister accurately in this small space or slice width.

With lens arrays using the lens microstructures or lens sets of theinvention, the lens microstructures can be configured so as to providethe function provided by a thick conventional lenticule by using anumber of thin lenses that are individually configured to focus on asubset of image slices (such as 1 to 3 slices rather than a whole set of4 to 12 or more slices). The lens arrays can be imprinted with the lensmicrostructures on a thin film at a very high rate of speed. In oneexample, a high quality image display assembly is achieved with a 3-milthick lens array having lens sets or microstructures on one sideprovided at 40 lens sets per inch (LPI) and an interlaced image on theother side. The interlaced image can be printed rapidly such as at up to2,000 feet per minute or faster on a web press or similar device. Toachieve a similar display capability with a conventional lenticular lensarray may require a frequency of 40 LPI and a thickness of about 80 milsor more. From these few example, it can be seen that the use of lensmicrostructures to generate a lens array provides a significant decreasein material costs, allows very thin lens arrays or substrates to be usedin numerous applications for which conventional lenticular material isnot practical, and greatly simplifies manufacturing by, for example,allowing printing of interlaced images at lower frequency or fineness.

More particularly, a lens microstructure is provided for use in lensarrays for displaying interlaced images. The lens microstructureincludes a substrate or layer of material that is transparent or atleast translucent to light. The structure further includes a linear orelongated center lens on a lens side of the substrate. First and secondsets of linear or elongated side lenses are positioned adjacent thecenter lens to extend parallel to the center lens. Each of the lenses isconfigured to provide a differing or unique focus direction or focusline such that the lens microstructure has an overall viewing angle thatis a combination of an angular distribution of the center lens andangular distributions from each of the side lenses (e.g., the focus ofthe structure steps out from the center lens with each side lens). Insome embodiments, each of the angular distributions differs but in somecases the angular distributions are substantially equivalent across thelens microstructure (such as a value from the range of about 1 to 10degrees). In some embodiments, an odd number of lenses are provided inthe lens microstructure with an equal number provided in each side set,and further, the cross sectional shape of the first side set ispreferably a mirror or reverse image of the second side set. Thethickness of the substrate may vary, e.g., with each successive lensfrom the center lenses being slightly thicker, or the thickness of thesubstrate as measured at the peak of thickest part of each lens may bekept substantially constant such as less than 15 mils and in some cases10 to 3 mils or less. The lens microstructure is configured for focusingon one set of slices in the interlaced image such as a segment set andeach of the lenses preferably focuses on a small subset such as 1 to 3slices that may generally be positioned beneath or adjacent thecorresponding lens. Lens arrays can readily be formed that include twoor more of such lens microstructures to display an interlaced image, andnumerous products that include such lens arrays and paired interlacedimages may be fabricated to practice the invention.

According to another aspect, an assembly is provided for displaying aninterlaced image. The assembly includes an interlaced image, which maybe digitally printed, web printed, or the like, with sets of elongateimage elements or slices. A lens arrays is provided with a first sideproximate the interlaced image such as a planar surface and a secondside distal the image with a plurality of lens sets. Each of the lenssets is paired with one of the sets of the image elements and includes anumber of linear or elongate lenses that are each mapped to a subset ofthe image elements in a corresponding one of the paired sets. Generally,each of the lenses is configured with a cross sectional shape thatallows the lens to focus light from the subset of image elements (e.g.,from one of the image elements). Each of the lenses may be configured toprovide a lens-specific viewing angle with a particular focus line, andin some preferred embodiments, the focus lines to the paired imageelement subset is chosen to differ from other lenses (e.g., each lenshas a unique focus direction such that the viewing angles are additiveto provide an overall viewing angle for the lens set). The interlaceimage may be printed directly onto the first side of the lens array(with or without a primer first being applied) or an adhesive layer maybe used to attach a separate substrate or sheet with the image to thefirst side of the lens array. In some cases, each of the lens setsincludes an odd number of lenses (e.g., 5 to 21 or more lenses), and thelens sets may be provided at a frequency in the lens array from 5 to 75lens sets per inch with a typical embodiment using a frequency of 10 to30 lens sets per inch, with the particular frequency being selected tosuit the interlaced image being displayed. An even number of lensescould be used to practice the invention. In this case, the sublenticulesor lens on either side of a center line of the lens set could havedistribution angles of plus/minus 2 degrees for example, but, it will beunderstood that this example does not need to be explained in detail asit is nearly equivalent to the case of a lens or sublenticule providedon such a center line of a lens set.

According to another aspect, an image display apparatus is provided thatincludes an interlaced image made up of a plurality of image elementseach having a particular or predefined width. A lens substrate isprovided in the display apparatus with a planar side positionedproximate to the interlaced image (e.g., the image may be printed to theplanar side or attached with a transparent adhesive). The lens substrateincludes a lens side distal to or opposite the planar side. The lensside includes numerous lens microstructures that are each made up of aplurality of lenses. Each of these lenses is paired or mapped to one ofthe image elements so as to focus light passing through the lenssubstrate to a width of about the width one of the image elements and todirect the light onto the paired one of the image elements (e.g. eachlens in a lens microstructures is used to display one of the imageelements in the interlaced image rather than a larger set of such imageelements). The image elements are grouped into segment sets including anumber of the image elements, and the lens microstructures each have thesame cross sectional shape that defines the shape of each lens in themicrostructure, with the cross sectional shape chosen to map each lenswith one of the image elements. In some embodiments, an odd number oflenses are provided in each of the lens structures such as by providinga center lens with a particular focusing direction (e.g., perpendicularto the planar side of the lens substrate) and side lenses extending fromboth sides of the center lens. The center and side lenses each haveunique or distinct focusing direction or focal lines that are selectedsuch that the angular distributions of all the lenses are generallyadditive or combinable to define an overall viewing angle (e.g., 20 to45 degrees or another useful viewing angle for displaying interlacedimages) for the lens microstructure.

In one embodiment, a method is provided for fabricating an assembly fordisplaying an interlaced image. The method includes providing a film ofmaterial that is at least translucent to light, such as providing a rollor sheet of a substantially clear plastic. The method continues withcreating a lens array in the film by forming parallel lens sets on afirst side of the film, and then bonding an interlaced image includingsets of elongate image elements to a second side of the film. Each ofthe lens sets may be configured as discussed in the preceding paragraphswith a set of lenses for focusing light from a subset of the imageelements in a particular mapped or paired set of image elements. Thebonding of the interlaced image to the film may include printing theinterlaced image directly onto the second side such as using webprinting at a rate of up to 2,000 feet per minute or greater, with theprinting facilitated by the very thin nature of the lens array that mayhave a thickness of less than 15 mils such as 1 to 5 mils or the like.Alternatively, the bonding may include bonding with a layer ofsubstantially transparent adhesive interposed between the second side ofthe film and the interlaced image (e.g., by using a thermally activatedadhesive provided on the second side of the film in a thermal laminationprocess that may include the use of nip rollers or otherwise pressingthe film and the interlaced image and/or a substrate holding the imagetogether). The creating of the lens array may include embossing of thelens sets into the first side of the film with a flat die orcylinder/roller engraved with a reverse image of the lens array such asafter the film is heated or with a heated roller or with cold embossingdie or roller. The creating may also include coating the first side ofthe film with a clear coating that is then embossed (e.g., a UV-curablecoating or a softer material layer that is more susceptible toembossing). The bonded combination may then be attached to a packagingsurface such as wrapper, label, decal, cover, or the like to allow easyuse of the combination in a display device or the devices (such ascards, posters, or the like) may simply be cut out in final form (or foradditional processing such as applying magnetic strips or additionallayers or further printing such as on the back side of a imagesubstrate).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a perspective view of an image display assembly or apparatussuch as a label, decal, or the like that may be applied to anotherstructure or used as a standalone device, with the imagery assemblyincluding a lens array and an interlaced image according to the presentinvention;

FIG. 1B is a perspective view of an image display assembly similar toFIG. 1A but further including an adhesive layer between the lens arrayand the interlaced image and a substrate upon which the image is printedor provided, with the adhesive layer being provided on either or boththe lens array or the interlaced image;

FIGS. 2-5 illustrate representative products that are shown to includethe image display assembly of FIG. 1A or FIG. 1B as a label/decal ormore integral part of a product sidewall;

FIG. 6 illustrates a cross section of one embodiment of portion of inimage display device showing a lens microstructure or lens set that maybe used in a lens array provided in the image display device of theinvention, with the illustrated embodiment using eleven lenses or microtenses in the lens set or microstructure as a representative, but notlimiting, example;

FIG. 7 illustrates an enlarged view of a portion of the image displaydevice of FIG. 6 illustrating in more detail an adjacent pair of lensesor micro lenses of a lens set or microstructure showing a vertical sidewall used to join and/or form side lenses of the lens array (with thecenter lens or micro lens typically being symmetric with a continuouscurve in cross section);

FIG. 8 illustrates an enlarged view of a portion of an image displaydevice, such as the device of FIG. 6, similar to FIG. 7 but showinglenses or micro lenses with a side wall that is not vertical (i.e., offvertical by a relatively small angle to facilitate manufacture of thelens assembly with such lenses in its lens sets);

FIG. 9 illustrates a ray tracing for the image display assembly of FIG.6 showing the effectiveness of having each lens or micro lens of a lensset or microstructure focus on a subset of an set of interlaced slicesor elements rather than on all of the slices in the set (such as on oneslice as shown (or 2, 3, or more slices but not all) rather than on allslices of the set (i.e., 11 slices in this example));

FIG. 10 illustrates in a more complete ray tracing for a single lens ormicro lens of the present invention that would be included in a lens setor lens microstructure that would in turn be repeated a number of timesto form a lens array of the present invention;

FIG. 11 illustrates with a cross section another image display assemblyemploying a differing embodiment of a lens set or lens microstructure ofthe present invention showing that the number of lenses ormicrostructures/micro lenses may be varied to practice the invention(e.g., 11 is not a requirement and other numbers such as 5 lenses may beused and typically the number of lenses in the lens set is selected asan odd number); and

FIG. 12 illustrates yet another embodiment of an image display assemblysimilar to that shown in FIG. 6 with eleven lens elements in its lensset or lens microstructure but differing in that the lenses or lenselements do not include vertical or near vertical side walls to maintaina constant thickness but instead the thickness increases with each lensfrom the center lens or lens element.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Briefly, the present invention is directed to lens arrays that can beused to reduce or even replace the use of conventional lenticularmaterial. With conventional lenticular material, numerous elongated orlinear lenticules or lenses are provided in a clear or translucent webor layer. Each lenticule is used to provide a viewing angle (e.g., 15 to40 degrees or the like and more typically about 20 to 35 degrees)through which a plurality of interlaced slices of an image segment arevisible to a viewer. For example, an interlaced image may be printed onthe smooth side of the lenticular material web with the set of slices,which may number 5 to 20 or more, for a segment of the image beingmapped to a particular lenticule such that the slices can be viewedseparately as the material or the viewer's line of sight is moved acrossthe viewing angle. The interlaced image with its interlaced image slicesor elements can in this way be viewed to achieve visual effects such as3D, animation, and the like. A significant problem with conventionallenticular material is that the lenticule (or the lenticular material)must be relatively thick to effectively focus onto the numerous imageslices paired with the lenticule. For example, the thinnest conventionallenticular material used today is at least about 15 mils but theprinting and mapping requirements generally have lead the printing andpackaging industry to use lenticular material or lenticules that are atleast about 20 mils thick.

In contrast, the lens arrays of the present invention can be thought ofas replacing each of these conventional lenticules with a lens set orlens microstructure. The lens set is configured with a number of lensesor “sublenticules” that are each paired with a smaller subset of slicesof a segment. For example, a conventional lenticule may be used toprovide a viewing angle to selectively view 15 image slices of a segmentof an interlaced image. A lens set or lens microstructure of a lensarray of the invention would, instead, use 15 lenses or sublenticulesthat are each mapped or paired with one of the image slices instead ofto all 1 image slices or elements. Each of the lenses of the lens setconfigured to provide a “step” or portion of the viewing angle, e.g., ifthe viewing angle is 30 degrees in the 15 lens example each lens wouldprovide a step of about 2 degrees such that the lens set provided thesame or similar viewing angle as a conventional lenticule. However, thethickness of the lens set can be significantly less than that of aconventional lenticule to provide the same or similar effect. Forexample, it is likely that lens arrays may be effective with thicknessesof less than about 15 mils and even less than about 3 mils (while, ofcourse, lens assemblies with thicknesses greater than 15 mils may beused in some applications).

The lens arrays of the present invention would include a number of thelens sets or lens microstructures similar in number to the lenticules oflenticular material, and the lens sets may be defined by frequencysimilar to lenticules at a particular LPI (e.g., lens sets per inch orlenticules per inch) and the overall pitch of the lens set or lensmicrostructure is often the same or similar to the pitch of thelenticule it is used to replace. An interlaced image may be produced fora conventional lenticular material such as for a 20 LPT lenticular lensmaterial, and the lens sets may be provided in a lens array with 20 lenssets per inch or at 20 LPI. The lens arrays produced according to theinvention are typically paired with an interlaced image that may beprinted onto the smooth side of the lens array (which may be formed fromplastic, glass, or other transparent to translucent material) or may beapplied to the back or smooth side of the lens array with an adhesive(e.g., with the printed interlace image provided on a substrate such asplastic, paper, or the like). The combination of the interlaced imageand the lens array forms an image display assembly, device, or productof the invention that produces high quality 3D, animation, and othervisual effects but with 50 to 90 percent or more reductions in thickness(i.e., with ultrathin lens arrays).

FIG. 1A illustrates an exemplary an interlaced image display assembly100 of the present invention. The assembly 100 may take the form of alabel, a decal, a poster, a billboard, a book cover, media insert,printing, or label (e.g., for CDs, DVDs, software, or other mediaproduct), a card (e.g., a debit, credit, smart, security, or other card)or nearly any product or device that is used to display images. Theassembly 100 is shown to include a lens array 110 that is mated with aninterlaced image 120 such as by the interlaced image 120 being printedonto a smooth or back surface of the assembly 110 distal or opposite thelens surface of the array 110. The lens “array” 110 of the invention isintended to be construed broadly to be a layer/sheet or layers/sheets ofa material such as plastic, glass, ceramic, or other transparent totranslucent material along with a lens surface formed on one side and asmooth or textured side opposite the lens surface.

The lens array 110 includes a number of lens sets or lensmicrostructures 116 that extend across one of the surfaces of the lensarray 110 (or may be provided in a select portion). The lens sets 116illustrated each include a number or plurality of linear or elongatedlenses or lens elements 117. The lenses 117 and useful configuration forthe lens sets or microstructures 116 are explained in more detail withreference to FIGS. 6-12. The interlaced image 120 is preferably printedonto or applied to the lens array 110 such that its sets of image slices126 are mapped or paired to the lens sets 116, e.g., with 1 to 3 or moreof the slices being positioned underneath or opposite one of the linearlenses 117. Note, the width of the lenses 117 and image slices 126 isshown to be much larger (or not to scale) in FIG. 1A as the lenses 117often will be less than 100 microns and more typically less than about50 microns. As explained further below, each of the lenses 117 in thelens sets 116 focuses a viewer's line of sight onto the paired subset ofslices from the full set of slices 126 from an image segment (i.e., noton all slices in the set 126), and such focusing will combine with theother lenses 117 of the lens set 116 to provide a predefined viewingangle for viewing the set of image slices 126 (e.g., 15 to 45 degrees oranother useful viewing angle).

Rather than printing directly on the lens array 110, it may be desirableto form image display assemblies by applying an interlaced image on asubstrate or with a plastic, paper, or other backer or liner onto thelens array 110. FIG. 1B illustrates such an image display assembly 150of the present invention. In the assembly 150, the lens array 110, whichis configured with lens sets 116, is bonded to a substrate 158 such as apaper, plastic, or the like sheet. The bonding is achieved with anadhesive 154 that may be applied to either the lens array 110 or to thesubstrate 158. For example, thermal laminating processes may be used toform the assembly 150 with the adhesive 154 being a layer of thermallyactivated adhesive applied to either the lens array 110 or more commonlyto the substrate 158. The adhesive 154 is activated by heat and thearray 110 and substrate 158 are mated together with pressure such asthat applied by a convention nip roller or the other pressure-applyingmachinery. The interlaced image 120 is applied or printed onto thesubstrate 158 prior to the bonding process and the bonding is performedto carefully map or pair the sets of image slices or interlaces with thelens sets 116 and the lenses 117 in each set 116. The assembly 150 maybe a standalone product such as a smart or credit/debit card or may beapplied to another structure as a label, cover, decal, or the like.

FIGS. 2-5 provide additional examples of products in which the imagedisplay assemblies 100 (or 150) may be used to practice the invention.FIG. 2 illustrates the use of the display assembly 100 provided on asidewall 210 of a package 200 between sealed ends 204, 208. For example,the package 200 may be a foil snack bag or a plastic or paper bag usedto package food, retail products, or the like. The assembly 100 may beapplied as a decal or label to the sidewall 210 or be provided as anintegral portion of the sidewall 210. FIG. 3 illustrates a similarpackaging 300 for a retail product such as a food product. A displayassembly 100 is applied to or provided as an integral portion of thesidewall 310 between sealed ends 304, 308, and the sidewall 310 may beformed of a metallic foil, plastic, paper, or the like as is commonlyused in the packaging industry. FIG. 4 illustrates a book, notebook,magazine, or the like 400 with pages 410 enclosed or bound to cover 412with front and back members 414, 416. The display device or assembly 100with the lens array 110 and interlaced image is attached to the cover412 on one or both members 414, 416 (e.g., front and back covers of abook, book jacket, magazine cover, notebook, or the like) or formed aspart of the cover 412 (e.g., the lens array 110 may be provided as partof the process to form a notebook cover or book jacket or the like).FIG. 5 illustrates a container 500 (shown as a bottle but could be acan, jar, jug, or any other container) with a sidewall 510, and a lensassembly 100 is attached to the container sidewall 510 such that theinterlaced image is visible through the lens array 110 with its lensesprovided in lens sets or lens microstructures 116. As discussed below,the lens assemblies 110, 150 are often particularly useful in packagingor products such as those shown in FIGS. 1A-5 because the overallthickness can be controlled to provide viewing of an interlaced imagewith an ultrathin lens array 110 (e.g., less than about 15 mils and, insome embodiments, a thickness selected from the range of about 10 milsto about 3 mils or less).

FIG. 6 illustrates a portion of an interlaced image display assembly 600according to one embodiment of the invention. The “portion” of theassembly 600 is selected to provide the details or configuration of oneexemplary lens microstructure or lens set 610. The assembly 600, asdiscussed with reference to FIG. 1A, would include a lens array with aplurality of such lens sets 610 that are provided in a side-by-sidemanner (e.g., with an edge lens of the lens set 610 abutting an edgelens of the next or adjacent lens set(s)). In prior art devices used toview an interlaced image, a lenticule 670 would be provided with aparticular thickness, t_(Lenticule), and a pitch to focus upon a set ofimage slices or image elements provided in an interlaced image 640. Incontrast, the invention addresses the limitations of such a lenticule670 by providing a lens set 610 with a separate sublenticule or lens foreach interlace or slice in the image 640. This results in a much reducedthickness, t_(Lens Array), for the lens set 610 (and the lens arraycontaining this and other lens sets that are typically configuredidentically to the lens set 610). The inventors have verified that thelens set or array thickness, t_(Lens Array), may be 50 to 90 percent orless of the thickness, t_(Lenticule), that would be provided for aconventional lenticule 670 that provides the same or similar function asthe lens set 610 (although the particular thickness of the lens array610 is not limiting of the breadth of the invention).

As shown, the display assembly 600 includes a lens set or lensmicrostructure 610 with a first side or surface including lenses and asecond side or surface 611 that may be smooth or textured and upon whicha printed image 640, such as an interlaced image, is printed (or appliedwith an adhesive such as shown in FIG. 1B). Generally, the process offorming the assembly 600 includes using a high or even the highestpractical resolution interlaced image 640 that can be printed anddesigning a lens for inclusion in the lens set 610 for each interlacedimage slice or element (or in some cases for 1 to 3 or more slicesrather than just one image element). Each lens of the lens set 610 isdesigned to send light from the paired slice underneath it or adjacentit precisely in a predefined or desired direction (e.g., designed tofocus the light reflected from the slice to be directed in a step of alarger viewing angle defined for the lens set 610 or over a smallviewing angle that differs but is adjacent or near to adjacent to thenext or adjacent lens in the lens set (e.g., a subpart of the viewingangle of the lens set 610)). Such a configuration of the lens set 610can be seen as a further improvement over a conventional lenticule 670in that it allows individual adjustment or setting of the angulardistribution from the interlaced pattern or image 640. A lens array madeof lens sets 610 can be made thin enough to be used as a wrappingmaterial or as thin as paper to be applied to another structure orprovided alone whereas conventional lenticules 670 are generally toothick and have more limited uses. Hence, the cost of material for a lensarray formed from a plurality of lens sets or lens microstructures 610is a fraction of the material cost for lenticular material withlenticules 670, which allows the display assembly 600 to be used to meetthe large market demand for labels and other thin packaging productsthat can be used to display interlaced images with motion, 3D, and flashimagery.

The lens set 610 is configured in the illustrated example to include anodd number of lenses (i.e., 11 in this example) with the number oflenses typically selected to match the number of slices of interlacedimage 640 that are paired with the lens set 610 such as the number ofinterlaces provided or each image segment in the image 640. As shown,the lenses of lens set 610 may be thought of as divided into a centerlens or lens element 612 and sets of side lenses 620, 630 (e.g., leftand right lens sets). The left and right lens sets 620, 630 mirror eachother in their configuration. For example, the lens 622 immediatelyadjacent the center lens 612 in the left lens set 620 is identical incross sectional shape as the lens 632 immediately adjacent the centerlens 612 in the right lens set 630 except that it is the mirror orreverse image.

The lens 612 is configured to focus on a paired slice 642 of theinterlaced image 640 through a particular viewing angle, such as afraction of an overall viewing angle selected for the lens set 610, andin a particular direction, such as when a viewer's line of sight issubstantially perpendicular to the image 640 and lens set 610. The leftlens set 620 and right lens set 630 each include one or more lenses thatare used to view the interlaced image 640 when the line of sight ischanged from perpendicular or near perpendicular. Each lens in the sets620, 630 provides its own step or particular viewing angle that focuseslight from interlaces or slices of the interlaced image that are pairedwith each lens (e.g., a subset of the interlaces such as one slice asshown in FIG. 6). For example, the lens set 610 may be configured toprovide an overall viewing angle of about 33 degrees. Each of the lensesin the lens set 610 including the center lens 612 would then be adaptedto provide viewing angle that is a fraction of this overall viewingangle. In one embodiment, the steps are substantially equal but in otherembodiments, the steps may be differ for at least some of the lenses(e.g., one viewing angle for the center lens 612, one viewing angle orstep for the next lens in both directions, one viewing angle or step forthe second lens in both direction, and so on or the angles may be variedfor only one or more of the lenses or lens pairs with the others usingthe same step value). In this 33-degree overall viewing angle example,each lens of the lens set 610 may provide an angular step/distributionor have its own viewing angle of about 3 degrees. Further, such angularstep or distribution is arranged to have a differing direction than theadjacent lens such that each lens of the lens set provides its ownunique viewing angle with a differing viewing direction. In thisfashion, the interlaced image 640 is displayed through the lens set 610with only one of the interlaces or slices being visible or displayed ata time or at a particular line of sight within the overall viewingangle. For example, the image element 642 under or paired with centerlens 612 may be displayed at a first position of the assembly 600 orviewer and when the line of sight is changed the image element 644 maybe displayed through lens 622 or the image element 646 may be thirddisplayed through lens 632.

As discussed above, each of the lenses in the lens set or lensmicrostructure 610 may be configured individually to focus on a pairedimage element or slice and/or to direct reflected light from such sliceor element in a particular direction and with a particular viewingangle. As shown in the example of FIG. 6, the lens set 610 includes acenter lens 612 that is generally symmetric about its center line (or aplane passing through its center). The lenses 622, 632 adjacent andabutting the center lens 612 provide a next step or angular distributionrelative to the viewing angle or angular distribution of the center lens612. For example, the center lens 612 may have a viewing angle of 1 to 5degrees or another value with its center substantially perpendicular tothe image slice 642. Then, each of the lenses 622, 632 may provide asmall angular step from this central viewing angle to provide twoadditional viewing angles or angular distributions for light from theimage slices 644 and 646 that are positioned underneath or adjacent thelenses 622, 632. In other words, the viewing angle provided by the threelenses 612, 622, 632 may be 9 degrees with each providing a 3 degreestep or subpart of the combined viewing angle, and within this combinedviewing angle, only one of the slices 642, 644, or 646 may be visible ata time depending upon a viewer's line of sight (although in many casesthere may at least some overlap such that portions of nearby slices maybe visible when a dominant or main slice is viewed).

A next step is added or provided by the contribution of lenses 624 and636 of the left and right side lens sets 620, 630. These lenses 624, 636provide the same angular step as the lenses 622, 632 or, in some cases,a smaller or large step. In the above example, each of these lenses 624,636 may provide another 3 degree step or angular distribution that isdirected so as to be additive to the viewing angle provided by lenses612, 622, 632 such that the overall viewing angle of these 5 lenses is15 degrees with differing ones of the slices of interlaced image 640being displayed or visible based on the light of sight (e.g., slice 648is paired with lens 624 and is generally only visible when the displayassembly 600 is positioned or the viewer moves to an angle that providesa line of sight falling within the 3-degree viewing angle of the lens624). Such step increases or additions to the overall viewing angleprovided by the lens set 610 are continued until outer side lenses 628and 638 are included, and the assembly 600 is formed by providingadditional lens sets configured similarly to lens set 610 to abut orcontact the edge lenses 628, 638 (e.g., another lens configured similarto lenses 638, 628, respectively).

To maintain the thickness, t_(Lens Array), of the lens set 610 at aparticular thickness (e.g., less than 15 mils for example) each of thelenses in the side sets 620, 630 is provided with a vertical side edgeas shown with edges 623, 625, 633, 637 for side lenses 622, 624, 632,636. An exemplary vertical side edge 623 is shown in FIG. 7 for lens622. The center lens 612 typically will also have side walls or edges613 to maintain the overall thickness of the lens set but these sidewalls may be very small relative to the edges 623, 625, 633, 637 shownfor the other lenses. The side edge 623 is typically vertical such thatthe edge 623 is substantially parallel to a plane passing through thecenter of center lens 612. FIG. 8, however, illustrates anotherembodiment of such side lenses that is configured to facilitatemachining or manufacturing of the lens sets. In this example, a lens set810 of a lens array or lens layer is shown to include a pair of sidelenses 822, 824, and a side edge 823 is shown to join the lens 822 tothe adjacent lens 824. The side edge 823 in this case is not verticalbut is instead offset or off vertical by an offset angle, θ, that ischosen based on tool or mold design to facilitate manufacture (e.g., alleasier removal or control binding of a cutting tool). For example, theoffset angle, θ, as measured from a plane parallel to a plane passingthrough the center of the center lens 612 as shown may be about 1 to 5degrees or larger and in one case is about 2 degrees.

Now, with reference to FIGS. 6 and 7, it may be useful to explain oneuseful design process for a constant thickness, t_(Lens Array),microstructure such as lens set 610. Initially, an overall pitch,P_(Lens Set), is selected for the lens set 610. A smaller pitch isgenerally preferable for obtaining a better image resolution. Next, thenumber of interlaced images or slices that will be displayed by the lensset 610 is chosen for an intended application, and in some embodiments,the number of slices of sets defines the number of lenses in the lensset 610 (e.g., with each lens being used to focus on a paired one of theimage slices or image elements). Typically the number is selected to bean odd number when a one-to-one relation is used for the lenses andimage slices, as this allows a single center lens to be used andcombined with side sets of lenses having equal numbers of lenses (whichcan be mirror or reverse images of each other). The pitch and number oflenticules are used to determine the width of each lens in the lens set.When the lenses are substantially equal in width, the lens width isdetermined by the following equation. Width of Lens=Overall Pitch orP_(Lens Set)/Number of Lenses in Lens Set.

A thickness, t_(Lens Array), is then selected such as less than about 15mils or a greater thickness. In some embodiments, the lens arraythickness, t_(Lens Array), is selected so it is related to the width ofthe lenses of the lens set 610 such as to be a little larger or thickerthan the width of each of the lenses (but, typically, much smaller thanthe thickness of a conventional lenticule, t_(Lenticule), used to focuson the interlaced slices previously chosen for the lens set 610). Theoverall viewing angle is selected and the viewing angle or angular stepor difference for each lens is chosen (such as by dividing the overallviewing angle by the number of lenses in the lens set 610), or theindividual lens angular steps or distributions may be set and thesesteps may be combined to define the overall viewing angle for the lensset 610. The values of the viewing angles for each lens and itsassociated image slice can be individually selected in some embodiments,which is not possible with conventional lenticular structures.

To start the theoretical construction of a lens of the lens set, a rayis traced from each interlace or image element position on the printedsubstrate 640 associated with the lens set 610 being designed. Aninitial trace is made to the center of lens element under constructionthat has temporarily been set to the desired thickness, t_(Lens Array).The slope of the lens element (e.g., of a segment of such lens elementbetween two knots) at that point is adjusted to refract the ray in thedesired angular direction for the lens element being generated, e.g.,the center lens or lens element 612. Then, a small increment along thedirection perpendicular to the lens set 610 axis is made in onedirection (e.g., left or right), and the starting point of the next lenssegment of the lens element or lens, is the ending point of the previouslens segment. The next or second segment of the lens element beingconstructed is connected to the end of the first segment and a slope isfound for the next or second segment to refract a ray to desireddirection (i.e., onto a particular location where an image slice isanticipated to be positioned). This process is repeated until a left orright boundary of the lens element is reached and the segment-by-segmentis repeated for the segments between knots in the other direction (rightor left) until the other boundary of the lens element or lens isreached. If a thickness overage occurs (e.g., over a preset overagelimit to achieve a desired lens array thickness), this thickness overagemay be subtracted and the process repeated to regenerate the lenselement. After completion of this lens element, a ray is sent from thenext or adjacent interlaced image slice to the center of a new lens orlens element, e.g., through the center of lens 622 or 632 aftercompletion of lens element 612. The slope of the segment of the nextlens element is adjusted so as to send the traced ray in a desiredangular direction (e.g., a step from the angular direction of the priorlens element such as a 3 degree or other angular step value from 90degrees when the prior lens element is the center lens 612). The surfaceof the lens set 610 is built up in this stepwise or piecewise fashionuntil a boundary of the lens set 610 is reached such as at the outeredge of lens 628 or 638 as shown in FIG. 6. Then, the process isrepeated in the other direction from the center lens 612 until the otherboundary is reached, i.e., the edge of lens 638 for example. Splinefitting may then be used to get a smooth interpolation between the knotsused to form each lens element of a lens set. This process of buildingeach lens or lens element of the set by extending calculated slopes overshort distances is explained in more detail with reference to theincluded program listing in the following paragraphs (e.g., thetechnique of generating the lens elements for each lens set may bethought of as step wise or iteratively constructing each lens element byslopes).

Such an iterative process may result in lenses that increase inthickness from the center lens 612. In some embodiments, a maximumthickness is chosen for the edge lenses 628, 638 and the center lens 612is provided at a thickness that is lower than this maximum, oralternatively, side edges such as edges 623, 625, 633, 637 (and edges613 on center lens 612) are provided to prevent or control the thicknessof lenses from increasing or to retain a constant thickness for the lensset 610. Should any lens or lens element of the lens set 610 include alens that causes total internal reflection instead of refracting rays ina desired direction, a linear interpolation of the slope may be made tothe end of the lens element (such as element 612, 622, 624 or the like)from that lens or lens element. Then, after a lens element has beendesigned, the process may be restarted by starting a ray at the nextinterlace or slice position and repeating the process, but designing thelens element for the desired refracted angle for the interlace or sliceunder consideration.

The lens set 610 of FIG. 6 illustrates a typical design result for theabove-described design or configuration process of the invention wherethe number of interlaced images or slices is eleven and the number oflenses or lens elements in the lens set or lens microstructure 610 isalso eleven. FIG. 7 illustrates in detail showing a lens 624 showinglens surface points 710 plotted or generated based on the ray tracingprocess described for focusing light from the slice or image element 648of interlaced image 640 using a known width for the lens 624, thicknessfor the lens array, t_(Lens Array), and, therefore, for lens 624, andangular distribution or viewing angle for the lens 624. Also, FIG. 7shows the connecting lines or line segments 714 generated for connectingadjacent pairs of the lens surface points 710. In one design process ofthe invention, after all the lens sets for a lens array have beendesigned, the end points of the segments 714 generated on the lenses arejoined by cubic splines or other useful methodology. This allows aprecise interpolation procedure to be made so that the surface of thelenses in the lens sets 610 of the lens array can be accuratelycalculated and plotted or drawn such as to a degree of fineness oraccuracy supported by machining process used to produce the lens arrayor the tool that is in turn used to form the lens array.

A computer program listing is provided at the end of this descriptionthat may be run to perform the design steps described in the precedingparagraphs for a lens set of the present invention such as lens set 610.The computer program may be run on nearly any well known computingdevice with a processor or CPU, memory, and a monitor, and the programmay be implemented with a computer system running the program with codedevices for making the computer perform the steps shown in the programlisting (not shown with a figure as such a block diagram is not believednecessary to understand the invention). The program listing provides thedetails of the algorithm that is used for designing or configuring alens set such as lens set 610 as described generally above, but itshould be noted that only the code or routines associated with thesedesign steps is provided with supporting subroutines that performrefraction, array handling, and the like being excluded for simplicityand brevity sake as these subroutines are well-known to those skilled inthe optical arts. Note, the program listing uses the term “lenticules”in place of “lens” or “lens element” as used in the description of thealgorithm provided above but this term is used at least in the listingin its more generic or broad sense as a synonym for lens.

The following is a brief description of the computer program or programlisting and provides some important ideas used to generate the lensmicrostructures of the invention. The entire lens array is typicallymade up of lens sets (microstructures). The lens sets have individualsub lenticular elements that are to be generated mathematically here orby the algorithms of the computer program. Each sublenticule or lenscross section is built up from short line segments each of which areconnected at one end to a previously calculated end. The slope of eachline segment is adjusted to refract a ray from the interlace locationthrough the segment in the desired direction. The free end of thatsegment, which slope was determined, is now the location of the start ofthe next segment. The initial starting point for each sublenticule isthe center of the sublenticule. After all of the points are determinedfor all the sublenticules, customary cubic spline fitting routines areuse to characterize the curves. See, for example, “Numerical Recipes:The Art of Scientific Computing,” William H. Press et al., 1986 (e.g.,at page 88 and other portions of the text).

The usual methods of program data entry are used to input the followingdesign parameters: pitch of the lens set; number of sublenticules inlens set; angular step of distribution from sublenticule tosublenticule; index of refraction of lenticular material; thickness oflenticules/lens array; slope limit; sidewalls (e.g., yes or no whichsets whether the thickness is held constant for the lens/sublenticulesin the lens set); and step size of knots in forming each sublenticule.The subroutines for ray refraction are well known optics procedures andomitted here in the sake of brevity and ease of explanation of the morepertinent features of the invention. Ray intersections of planes andcubic splines curves are also omitted as these are standard routinesused in computer graphics programs. The methodology starts at thedesired thickness in the center of each sub lenticule and calculateseach part of the lenticule first in the negative direction and thenrestarts in the center and calculates in the positive direction usingthe endpoints of the sublenticule. The endpoints were previouslycalculated from the pitch of the lens set and the number of thesublenticules.

In some embodiments, lens arrays of the invention such as a lens arraywith lens sets or lens microstructures 610 is formed by first machiningor generating a mold that is used to form the lenses of the lens setsand lens arrays such as from plastic or the like. The mold may begenerated using an air bearing lathe and precise diamond tooling. In oneimplementation, the lathe and tooling may have a 0.01 micron or similarresolution to insure that a good optical surface is obtained from themold. A number of materials may be used for the material of the moldsuch as a soft brass that can be cut by a diamond to form the tool forthe plastic (or other transparent to translucent material) lens array.In some cases, the mold or forming tool for the arrays may be made of amaterial that is relatively soft and that may not be useful forproviding many impressions as would be required for high productionruns. In these cases, electroforms may be made such as in a two stepprocess to get the correct polarity of the structure. Further, in somecases, the straight side walls of the side lenses such as side wall 623shown in FIG. 7 may cause difficulties with release (e.g., electroformrelease from the tool). To reduce this possible issue, the side wall maybe designed with an angular offset or slope, θ, from vertical as shownin FIG. 8 with side wall 823 (e.g., an offset, θ, of 1 to 5 degrees ormore).

A check on or verification of the effectiveness of the design of a lensarray such as array 610 of display assembly 600 may be obtained by anon-sequential ray trace as shown in FIG. 9. The rays 910 are shown tobe focused on or reflected from the image elements or slices of theinterlaced image 640 through the lens array 610. Each lens such ascenter lens 612 and adjacent side lenses 622, 632 each provide anangular distribution or lens-specific viewing angle, Ø₁ to Ø₁₁, with aunique direction (e.g., provide a stepped angular distribution relativeto the next or adjacent lens). The overall viewing angle, ⊖_(Viewing),for the lens array 610 is provided by a combination of theselens-specific viewing angles, Ø₁ to Ø₁₁. For example, with 11 lenses asshown, each lens-specific viewing angle would be about 1/11 of theoverall viewing angle (e.g., 2 degrees when the overall viewing angle is22, 3 degrees when the overall viewing angle is 33 degrees, and so on).A limited range of rays was traced in FIG. 9 to show more clearly theproperties of the lenses of the lens set 610 in providing focusing onjust a subset of the interlaces of a segment rather than all of theinterlaces or image elements (with the subset being just one imageelement under each or pair/mapped to each lens of the lens set 610 inthe embodiment of FIG. 9).

FIG. 10 illustrates further ray tracing for a particular lens 1014 suchas a center lens of a lens array 1010 (with the other lenses not shown).The lens 1014 provides viewing angle, ⊖_(Viewing), that would becombined with the viewing angles of the other lenses of the lens array1010 to provide an overall viewing angle. The main distribution 1020 ismade up of rays emitting from the pairs of interlaces and lens elementsof a lens set. Distributions 1024 and 1028 are the result of rays thatpass through neighboring lens elements of the lens set. The maindistribution of rays 1020 is shown to be focused on the single slice orimage element 1018 from a relatively large distance away from the lens1014, with wider angles or rays falling outside or toward the edge ofthe viewing angle having reduced brightness and being out of the mainviewing angle (e.g., the lens-specific viewing angle). The rays at thewide angles at 1024, 1028 are also focused on the slice 1018 but aretypically outside the viewing zone for the lens 1014.

The lens set 610 of the display assembly 600 of FIG. 6 illustrates theuse of eleven lenses for focusing on eleven slices or images from aninterlaced image. This is intended to be a useful example of how toimplement the invention but not as a limiting example because the numberof slices in the sets or segments of an interlaced image may vary, andit may be useful to maintain a one-to-one relationship between thelenses of a lens set and the slices of an interlaced image.Alternatively, the ratio or relationship of lenses to the number ofslices or image elements in an image or segment set may be varied. Forexample, in the example of 11 slices, 3 to 11 or more lenses may be usedto provide lenses that focus on a subset of the slices but not on allthe slices of an image or segment set of an interlaced image. Morespecifically, if five lenses were used to view eleven slices in eachlens set of a lens array, the center lens could be configured to viewthree slices over its angular distribution or lens-specific viewingangle while two lenses could be provided in each side set of lenses.These side lenses would be mirror images of each other, and it may beuseful for each of these side lenses to focus light from two slices at adesired direction (e.g., with each focusing direction being unique ordifferent from other lenses of the lens set) such that each of theslices of the image or segment set was displayed by the five-lens lensset. This is possible by tuning or configuring each lens of the lens setto provide its own angular distribution or lens-specific viewing anglethat combine or are additive to create the overall viewing angle of thelens set or lens microstructure.

While the number and combination of lens numbers and image slices aretoo numerous to detail here and would be apparent to those skilled inthe art with the above description, it may be useful to provide at leastone additional example of a lens set configuration. FIG. 11 illustratesanother interlaced image display assembly 1100 with the view shown beingof one paired lens set 1110 and set of slices of a segment or image fromthe interlaced image 1140. As discussed above, a lens array for theassembly 1100 would typically include at least two of such lens sets1110 that would be repeated across the lens array or lenssheet/substrate/layer of the assembly (e.g., lens sets may be providedat a density or frequency of up to 40 or more LPI (lens sets per inch)with 10 to 30 LPI being useful in many embodiments). The assembly 1100includes a lens set 1110 with five lenses shown as a center lens 1112, apair of side lenses 1115 in a left lens set 1114, and a pair of sidelenses 1118 in a right lens set 1117. In this embodiment, the centerlens 1113 includes a pair of side walls 1113 that connect it to adjacentlenses 1115, 1118 while maintaining a desired thickness for the lens set1110 (i.e., the lens set 1110 is a “constant” thickness lens set inwhich the thickness of the lens set as measured at the “peak” orthickest portion of each lens is substantially the same throughout thelens set). Likewise, the adjacent lenses 1115 and 1118 to the centerlens 1112 have side walls 1116 and 1119 to join or connect them to thenext lens of the side lens sets 1115, 1117 while maintaining the desiredthickness for the lens set 1110 and a lens array containing the lens set1110.

The lenses 1112, 1115, and 1118 may be configured or generated to have aparticular cross sectional shape as shown with the configuration ordesign process discussed above and detailed in the algorithm shown inthe program listing. The lenses 1112, 1115, 1118 are paired or mapped toimage elements or slices 1144 in the interlaced image 1140. In thisexample, a single lens is paired with each slice 1144 (but a lens may beused to focus light from more than one slice 1144). In one embodiment ofthe lens set 1110, the lenses 1112, 1115, 1118 are each designed todeviate rays 8 degrees apart relative to the neighboring or adjacentlens in the lens set 1110. In other words, each lens of the lens set1110 is adapted to provide an angular distribution or lens-specificviewing angle of about 8 degrees and the direction or focus line (ormain direction) for each lens is selected such that the angulardistributions are additive over the lens set 1110 (e.g., generally donot overlap or only overlap a relatively small amount). Hence, the lensset 1110 of this example would have an overall viewing angle of about 40degrees (or 5 times 8 degrees). It should be again noted that theangular difference or lens-specific viewing angle does not have to beconsistent across the lens set 1110, and in some cases, each lens of theset 1110 may have a different angular distribution. More typically, whenthe angular difference or distribution is varied, a regular pattern isused such as by setting the center lens 1112 at one lens-specificviewing angle, the pair of lenses on either side of the center lens 1112at a different lens-specific viewing angle, the pair of lenses adjacentto these two lenses moving outward in the lens set 1110 at yet anotherlens-specific viewing angle, and so on. In other cases, the center lens1112 has one angular distribution and each of the side lenses 1115, 1118has the same angular distribution (but, of course, with a differing maindirection or focus line).

The display assembly 1100 of FIG. 11 is also useful for showing that thelens set 1110 may be paired to the interlaced image 1140 by adhesive ora bonding layer 1130. As shown, the lens set (or lens array of which itis one component) 1110 includes a planar side 1120 opposite the lensside, and this side abuts an adhesive layer 1130 (such as a thermallyactivated adhesive such as a polyethylene common in thermal laminatingprocesses). The adhesive layer 1130 bonds the lens set 1110 to theinterlaced image 1140 which is made up of the image slices 1144 (e.g.,an ink layer) and a substrate or backer layer 1148, which may beplastic, paper, or other material upon which the ink of image slices1144 is printed or provided. In manufacture, the adhesive 1130 may beprovided on either the lens set/lens array 1110 or the interlaced imagelayer 1140. In one example, though, the adhesive is provided on theinterlaced image layer 1140 (and, in some cases, a protective layer orcoating formed of plastic or other transparent to translucent materialmay be provided over the ink of slices 1144 such as when the adhesive1130 is a thermally activated adhesive). In other embodiments, theinterlaced image slices 1144 are printed directly onto the surface orside 1120 of the lens set/array 1110 and a plastic or other materialbacking 1148 is applied with an adhesive that is provided with thehacking 1148 (e.g., the position of the ink of slices 1144 and theadhesive 1130 is reversed in the assembly 1100), which is common withgift, smart, credit/debit, and other cards and other fabrication ofconventional lenticular material products.

The lens set embodiments previously discussed with reference to FIGS.6-11 each have a lens thickness that is maintained constant orrelatively constant across the lens set or lens microstructures (andhence, across a lens array or sheet of lens material of the presentinvention as the lens sets are repeated), and this typically resulted inthe use of side walls being used to join the lenses (e.g., a verticaldrop to the next or adjacent lens rather than allowing the lensthickness to exceed a preset desired lens or lens array thickness). FIG.12 illustrates another embodiment of an interlaced image display device1200 that uses lens sets 1210 in which no side walls are used to joinlenses and the lens thickness increases with each lens from the centerlens 1212. As shown, the assembly 1200 includes a lens set 1210 (orplurality of such lens sets 1210 providing a lens array) with a lensside and a back or opposite side/surface 1219. In this embodiment, aninterlaced image 1220 is printed directly on the surface 1219 with a setof slices 1226 of an image segment but in other embodiments a primer, anadhesive, and/or other transparent/translucent layers may be interposedbetween the surface 1219 and the image 1220.

The lens set 1210 includes eleven lenses but the number may be modifiedto practice the invention, and the lens set 1210 is made up of a centerlens 1212, a left set 1214 of side lenses 1215, and a right set 1216 ofside lenses 1217. In this embodiment, the left set 1214 and right set1216 have cross sections that are selected to be mirror or reverseimages when viewed from a plane passing through the center line of lens1212. The thickness, t_(Center), of the center lens 1212 is less thaneach of the side lenses 1215, 1217 which have thicknesses, t₁, t₂, . . ., t_(x), that increase in a stepwise fashion as the outer edges of thelens set 1210 are approached. In this manner, the lenses 1215, 1217 canbe formed without requiring a sharp or abrupt edge but can instead be acontinuous curved surface between the end points or edges of adjacent orneighboring lenses.

To generate the cross sectional profile of the lens set 1210, the designor generation algorithm discussed above can be used with some minormodifications (and see the program listing at the end of thisdescription). An exemplary design or generation process may begin withsetting a desired thickness, t_(Center), for the center lens (or innerpair of lenses if an even number of lenses is used) 1212 for focusinglight from the inner image element or slice 1226. The center lens 1212is generated as discussed for center lens 612 of FIG. 6 with theexception that when the edge of the lens 1212 is reached the end pointbecomes the starting point of the next lens (i.e., the adjacent one ofthe side lenses 1215, 1217). Another difference is that the thickness,t_(Center), of the center lens 1212 is not forced on the succeedinglenses of the side lens sets 1214, 1216. As shown in FIG. 12, thisresults in a gradual climb with each successive lens from the centerlens 1212 being slightly thicker. A ray tracing performed for thestructure 1210 was performed and showed that the lenses 1212, 1215, 1217effectively focused light from the paired slices 1226.

As shown in FIG. 11, a wide variety of lens arrays with differingnumbers of lenses or sublenticules, viewing angles, thicknesses, andother parameters may be formed according to the present invention, withor without use of the lens array generation algorithm described herein.With this in mind, the inventors generated a number of additional lensarray models and performed ray tracings of these modeled lens arrays orlens microstructures of such arrays to verify their functionality infocusing each lens upon one or more image within a larger set ofinterlaced images. These arrays and their tracings are not shown inadditional figures because the inventors believe with reference to FIGS.6-11, the program listing, and the corresponding description that theirconfiguration and the method of generating such arrays will be clear toone skilled in the art.

In another modeled and tested (i.e., via ray tracing) lens array of theinvention, the lens array included lens sets or microstructures with 19lenses including a center lens and right and left lens subsets of 9lenses each. The overall viewing angle of each microstructure was about38 degrees with each lens providing an angular separation or step ofabout 2 degrees. The overall pitch of the lens set was 0.5588millimeters (mm) and the array was provided at a relatively constantmaximum thickness of about 0.0508 mm. Sidewalls were included in theside set lenses with an angle of 88 degrees (or 2 degrees fromvertical). The lenses were formed in the generation algorithm using 22steps for each lenticule (with a step size or DelX of1.33684210526316E-03) with a slope limit of 76 degrees. Ray tracing withthe assumption that the material used to form the lens array had anindex of refraction of 1.4 was successful in showing focusing on animage placed under the center of each of the 19 lens in the lens array.

In a similar embodiment, a lens array was modeled in which each lensmicrostructure had the same number of lenses in its lens sets (i.e., 19lenses in each lens set) and the same thickness and overall pitch.However, in this lens array, the overall viewing angle was about 76degrees and each lens provided an angle step size of about 4 degreesrather than 2 degrees as used in the prior embodiment. Other parametersincluding the number of steps and step size used to form or generate themodeled lens of the lens microstructure were retained as was the indexof refraction of 1.4. The lens set or lens microstructure was againsubjected to ray tracing, and the results again showed very accuratefocusing upon a single interlaced image positioned under or on the backor opposite side of the lens array (e.g., as would be the case if theinterlaced image were printed or otherwise positioned to abut the planarback side of the lens array). This embodiment is useful for showing theability to select a particular number of lenses for each lens set andthen to design these lenses to each have a structure to provide adesired overall viewing angle for the lens set by providing a particularangular distribution or step for each lens in the microstructure.

In another embodiment of the invention, a lens array was modeled (i.e.,generated using the generation algorithm described herein) that usedlens sets with 7 lenses including a center lens and side subsets eachhaving 3 lenses. In this embodiment, the following parameters were used:lens set pitch of 0.2 nm; a lens array thickness of 0.0762 mm; anangular step size (or angular separation) of about 5 degrees to providean overall viewing angle of about 35 degrees; an index of refraction forthe lens array material of 1.4; vertical sidewalls (i.e., at 90 degreesfrom the planar back side of the lens array); and 22 steps used togenerate each lens with a step size of 1.29870129870913E-03 mm and slopelimit of 74 degrees. The modeled or generated lens microstructure wassubjected to ray tracing to test its ability to focus light upon asingle slice or image element from a set of interlaced images, and theray tracing plot proved the efficacy of lens arrays using thisembodiment of lens sets or microstructures to display interlaced images.

An additional lens array embodiment was modeled that altered this 7 lensper lens set embodiment by modifying two parameters. Specifically, theindex of refraction for the lens array material was changed to 1.64 toshow that the lens arrays of the invention can be formed from a varietyof materials and still provide desired focusing results. Also, the anglestep size or angular distribution was increased to 6 degrees such thateach lens set provided a viewing angle of about 42 degrees rather than35 degrees. The lens microstructure generation algorithm was utilized togenerate a lens set or microstructure with these parameters orcharacteristics, and ray tracing of this modeled lens set verified thatthe lens set is capable of focusing light upon one or more interlacedimages positioned adjacent each lens over the desired viewing angle of35 degrees with each lens providing an angular step or separation ofabout 6 degrees. From these and the previous specific examples, it willbe appreciated that the general concepts of the lens sets ormicrostructures used to form lens arrays for displaying interlacedimages can be used to generate a huge variety of lens arrays simply bealtering one or more of the design parameters. This allows a designer toselect the parameters that are important to them such as viewing angle,number of interlaced image elements that need to be displayed under eachlens microstructure, or the like and then to generate lenses for eachmicrostructure with a geometry that provides these desired results orsatisfies the input parameters.

The use of lens microstructures or lens sets in lens arrays to bend andfocus light in order to view interlaced images provide an effectivealternative to conventional lenticular technology. Lens arrays withproperly formed/generated micro lens structures can replace lenticularlens arrays and allow viewing of interlaced images. Significantly, theuse of lens arrays of the invention can decrease lens mass and/orthickness such as up to 90 percent or more reductions. The lens designcriteria of conventional lenticular materials (i.e., including therequirement that the lenticule provide a thickness that allows focusingon a large set of interlaced slices) do not apply to these structures asthe lens sets are used to replace the much larger and thickerconventional lenticules, but the lens microstructures or lens setsremain optically sound for imaging and generally are not diffractive.The micro lens set designs follow typically optical characterizationssuch as Lambert's law and Snell's law, but the lenses of each lens setact together as a group to display interlaced images paired or mapped tothe lenses, thereby replicating the function of traditional lenticularlens arrays. However, they are not traditional lenticular lens arrays inpart because the lens sets are not uniform lens arrays with alllenticules having identical cross sections but instead, each lens in alens set or lens microstructure is configured to provide a unique focusline (or main direction) over a lens-specific viewing angle.

The lens arrays and their plurality of repeating lens microstructurescan be formed from plastic, glass, ceramics, or other transparent totranslucent materials from or using coatings, films, and/or othersubstrates. The lens microstructures can be custom designed for thecombination of interlaced images and, as discussed, may have apre-engineered overall viewing angle and lens-specific viewing angles orangular distributions and are also pre-engineered as to the number ofinterlaced images under the lens set or lens microstructure. Unlikeconventional lenticular lenses, a lens array of the present inventioncan be used to replicate the functionality of a very course lenticularlens array without adding much (or any) mass to the array (e.g., withoutrequiring a thicker lens array as the lens array becomes coarser or alower LPI). For instance, a 15 LPI conventional lenticular lens arraywith a 22-degree viewing angle would likely require about a ⅜″ thicklens array if made of acrylic. In contrast, a lens array with the lensmicrostructures of the invention can be made at about 3 mils thicknessbut yet perform similarly to the conventional lenticular lens array orbetter but yet use less than about 5 percent of the mass or lens arraythickness.

It may be useful to elaborate at this time on exemplary methods ofmanufacturing and/or tooling the lens arrays of the present inventionand more particularly, the lens sets or lens microstructure of thepresent invention as well as image display devices and products thatincorporate such lens arrays. In some embodiments, the lensmicrostructures of a lens array can be engraved in a cylinder or plate,with care taken to be extremely accurate to create the proper optics. Apreferred method of engraving is using an air bearing lathe and customdiamond tooling. Air bearing lathes operate by spinning the cylinder orcylinder with shim or plate on a cushion of air rather than bearings orother mechanical devices that can have worn or gear slop or play. Forthe formation of the tool to create accurate lens microstructures of alens array, it is preferable to provide accuracy at the micron level oreven at the angstrom level.

In order to create an accurate embossing tool, custom diamond toolspre-engineered to a desired radius are made. As the lens elements arenot usually defined by a particular radius, the cutting tools contourthe embossing tool tangent to different parts of the radius tool asneeded by the design determined by the usual cutting path of numericalcontrol or N/C programmed machines. These tools mirror the desireddesign such as an array with lens sets shown in FIG. 6, 11, or 12. It istypically useful to tool night and left hand diamond cutters to make thestructure. The center lens is typically symmetrical, and the outsidestructures or lenses to the right and left (i.e., in the left and nightside lenses) have different angles or angular distributions per thedesired design of the optics of the overall structure. As discussed, thedesired viewing angle of the total lens microstructure is a combinationof all of the sub-structures in each lens set. Each of the micro lensstructures has a different angle with a different or unique focusdirection and is tooled differently to complete the lens structure. Eachsub-lens structure is designed to complete the focus of the master lensstructure. Each of the master lens structures or lens sets simulates thefunction of a conventional lenticule or lenticular lens. The design ofthe lens structures are the result of testing various possible designsand structures and determining what happens to the light rays going intoand back out of the structures to the viewer.

Each of the microstructures may be as small as 10 microns or less andusually would be about 25 to 50 microns or more across. In someembodiments, each of the lens microstructures has a symmetrical centermicro lens and a set of right hand and left hand lenses that mirror eachother in design. Further in a typical embodiment, each of the substructures or lenses on each side has an angle step that ispre-determined and the combination of the lens angular distribution orlens-specific viewing angles total the desired overall viewing angle ofthe lens microstructure or lens set. Prior to tooling or manufacture,the lens microstructures are adjusted/tuned and tested in a computerprogram, such as the program listing provided herein and/or with raytracing programs, to verify where light rays focus to the image and backto a viewer. Each lens or microstructure within a lens set may have begenerated by providing or plotting 2 to over 100 data points, and theseplotted data points can be adjusted for the numerous (e.g., millions) ofpossible combinations so as to enhance the use and function of the microlens structure.

While one current known method of creating the embossing or extrusiontool, which in turn is used to form the lens arrays, is by using diamondtooling, other embodiments use laser etching or photo etching intonickel, carbon, copper or other metals to form the embossing orextrusion tool or to form molds. These alternative methods can result inaccurate tooling but may require more extensive testing and developmentto provide the accurate three-dimensional shapes necessary to create thedesired lens microstructures needed for lens arrays of the invention.

With the embossing tool, extrusion tool, or mold formed, the fabricationof lens arrays with the lens sets or lens microstructures of theinvention can be performed or completed. The lens microstructures andarrays with pluralities of such microstructures may be created by anumber of manufacturing methods and into or using a variety ofmaterials. The materials used for forming the lens arrays may be glass,nearly any type of clear (i.e., transparent to translucent) plasticincluding but not limited to PET, propylene, OPP, PVC, APET, acrylic, orany clear plastic, and/or a ceramic. In many embodiments, the preferredbase material is a plastic, and the plastic may be extruded, calendared,cast, or molded with the tools formed as described above to provide amirror image of the lens sets or lens microstructures arranged in a lensarray (e.g., a plurality of side-by-side, linear lens sets selected innumber to provide a desired frequency such as 10 to 50 LPI or anotheruseful frequency to suit a particular interlaced image).

One preferred application or fabrication technique is inline embossingat high speeds using a roll embossing tool. In this embodiment, a filmis cast or extruded, and a pattern providing the lens array is placedinto the film with a heat or chilled roller. A good film for thisapplication is usually a stable film such as a PET, cast propylene film,or the like. These films can be embossed in thin films of less than onemil to 3 mils or more. A preferred thickness for lens arrays is in thetwo to five mil range. In this application, the film thickness with itslens microstructures can be pre-engineered to focus directly on the backof the film. The film itself can be printed in a web or roll form atvery high rates of speed (e.g., over 2,000 feet per minute) in wide webapplications. To form image display devices (such as labels, decals,cards, or the like), the film or sheet with lens arrays is mirror orreverse printed with the corresponding interlaced images. At this point,individual devices or products may be cut from the combined rolls orsheets. The film also may be embossed in a thickness that is less thanthe desired thickness for focus and printing so that an adhesive can beadded to the film (i.e., between the lens array and the image slices) sothat in combination the adhesive and the film provide the thicknessrequired to focus to the interlaced images properly. The index ofrefraction of both the film and the adhesive in combination is takeninto account in the overall formula or algorithm discussed above forgenerating lens sets or lens microstructures. In some cases, a film mayalso be co-extruded with a coating such as a UV, solvent, or water basedcoating that may be embossed or extruded on the film with the microstructures built into the coating.

With a pre-made film, one can also print in a sheet or web form. Thefilm can be applied over the printed (interlaced) image after the fact.This can be done using equipment such as thermal film applicators like Dand K, Bellhoffer and the like in which the film is heated and theadhesive is a hot melt chemistry made with EVA/polyethylene and isactivated and applied in register to the printed and interlaced images.This can be done in line in a web process or in a sheet environment.

While extrusion techniques typically do not provide extreme filmthinness and are primarily used to make plastics no thinner than 6 milsand usually between 6 and 30 mils, extrusion processes combined with thelens microstructures of the present invention can provide a much thinnerlens array as opposed to traditional lenticular lens structures, whichleads to a significant material cost savings as well as providing lenssheets or arrays that are very flexible and easy to apply to otherstructures/products. For example, a lens sheet or array can be extrudedat a very coarse LPI for billboards and other applications in arelatively thin structure. In one implementation, a 1 or 2 LPI lens fora billboard may require a lens structure of over 1″ thick plastic iffabricated with conventional lenticular lens material, but this can bedone with a microstructure lens array of about only about 20 milsthickness. Hence, extruded plastic lens arrays of the present inventionare economical with respect to material costs and practical while aconventional lenticular lens array in a thickness of over 1 inch is notcost effective and is impractical.

Another method of manufacturing image display assemblies with lensarrays of the invention is to print the interlaced images on paper orplastic and then either in line or off line, printing or applying acoating, which may be an e-beam, UV, or water-based coating. The coatingis applied in a predetermined thickness, and the lens microstructuresmay be embossed into the coating to form the structures and a lens arrayover the interlaced images at high speed. Again, this may be done inline or off line in a sheet fed press such as a Heidelberg or Komoripress or a web press such as a Goss, Heidelberg, or other type of flexoor web offset press. Further, while most embodiments using an embossingtool would use a roll or cylinder for the embossing tool, in any of theabove embodiments, it is also possible to use a platen press or flatplate to emboss films or coatings.

With these various methods of manufacturing lens arrays and productsincluding the arrays generally understood, it may be useful to furtherexplain some of the preferred methods of manufacturing lens arraysaccording to the invention beginning with film embossing. Film embossingis a preferred method of manufacture that is anticipated to be easilyadapted for producing lens arrays or material with the lens sets of thepresent invention. In this embodiment of manufacture, there are severalmethods of performing the embossing. Embossing can occur at the time afilm is cast, calendared, or extruded. Normally, the embossing is donein line with a chilled embossing roller while the film is still hot. Thepressure is applied between a bottom and top roller. For example, thebottom roller may be a polished roller and the top roller an engravedroller, e.g., made out of a nickel-coated copper that is accuratelymachined in an air bearing lathe. The hot film, which may be propylene,PET, cast PVC, calendar PVC, cast propylene, PETG, or any combination offilm or co-extrusion. While the preferred substrate or film may bepolyester or PET, any of the substrates can be used. PET films tend tobe more stable and maintain the desired structure through the printingand embossing process better than many of the other films. It is alsoimportant to note that the refractive index of the material chosenpreferably is matched to the desired structure to make microstructuresthat provide accurate focusing on interlaced images slices. Dependingupon width, temperatures, pressures, and other factors, the film may beembossed at up to 10,000 feet per minute. One reason for using a filmroller in the film embossing process is that the molecules in the filmform and freeze into place forming the microstructures more accuratelywhen a hot film is embossed with a chill roller regardless of theprocess.

In some embodiments, cold film is used. Cold film can be heated andembossed with a hot roller forming the microstructures. This is normallydone at slightly below the melting temperature or at the meltingtemperature of the film. The speed at which this embossing can be doneis based upon the heat and pressure of the equipment available. Forexample but not as a limitation, if a substrate melts at about 300° F.,embossing is preferably done at about that temperature and, in somecases, at about 6,000 feet per hour.

In other embodiments, cold embossing is used to form lens arrays of thepresent invention. Cold embossing can be done using extreme pressuresbetween nip rollers while narrow web widths are easier and require lesstonnage. It is possible, however in some embodiments to emboss in wideweb at up to and over 60-inch web widths. Such cold embossing of thelens arrays into plastic or other material substrates can be done atfairly high rates of speed such as up to about 10,000 feet per hour ormore. This is done much the way holographic embossing patterns areembossed in film. The structures tend to be accurate, but the life ofthe tool is sometimes not very long due to the higher pressuresutilized.

Film embossing to form lens arrays of the invention may also includeplaten embossing. Flat dies are engraved in copper magnesium, nickel,and other metals. These dies are placed in equipment such as Bobst diecutters and Heidelberg's, Kluges, and other equipment manufacturers' diecutters, punches, presses, or the like used in platen embossing. Thefilm may be fed through in rolls or in sheets and embossed with heat andpressure or just pressure to form the lens sets or lens microstructureson a side of the film or substrate. The microstructures can be embossedonto any of the films using pressure and or heat and appropriate dwelltime to form the microstructures. A significant tonnage or high pressuresuch as needed to emboss holograms is generally used to emboss the filmin the case of platen embossing. In this embodiment, one can have “spot”lens structures that can be registered to the printing in a way suchthat the lens does not always appear over the printing.

For embossing of the lens microstructures to be effective, the flat diesor rollers/cylinders have to be accurately formed to includes a reverseimage of one or more of the lens microstructures (e.g., a number ofparallel lens set extending side-by-side to provide a lens surface of alens array). In addition to using diamond or other cutting tools to formthe dies or embossing rollers, one of the methods of manufacture is theuse of photo-etching for the engraving of the flat embossing dies orembossing cylinders or rollers. A standard method of photoengraving orphoto-etching is done by using an emulsion over a metal or polymersurface and then exposing the areas in which the photo emulsion may beexposed to UV light. The areas that are exposed generally remain in tact(but it can be the opposite effect), and the remaining area is exposedand unprotected. An acid bath is generally used to wash away theunprotected areas (i.e., the areas that lacked the protective emulsion).The metal or polymer with a pattern defined by the emulsion is leftbehind leaving raised surfaces with a desired pattern and contour (e.g.,a reverse image of a particular set of lens microstructures desired fora lens array or for a number of lens arrays as it is expected thatnumerous lens arrays may be embossed into a film or sheet at one time inmanufacturing processes, paired with a plurality of interlaced images,and later cut out to provide display devices such as cards or the like).The process is generally used to make etched dies for embossing papersand foils where some three-dimensional relief is needed. Normally, thisprocess is done with a stationary light source.

In order to complete more complicated diffraction gradings for imagingand non-imaging applications for lenses including diffraction gradings,it is preferable in some embodiments to take this photo emulsiontechnology several steps further. In order to create accurate depths inmetals and polymers, processes used should be accurate for length ofexposure of the light source, strength of the light source, compositionof the photo-polymer involved, and other factors. Using lasers as thelight source in place of or in addition to UV lights gives a moreintense and controlled exposure, and also provides enhanced control andthe angles useful to create exposures not through film (although filmcan be used) but controlling the angles of the exposure in an X axis andan Y axis (or X-Y coordinate system) over the polymers, metals, andphoto emulsions. Actual metals used for the cylinders or dies may bemagnesium, nickel, copper, carbide, or other metals or polymers such ashybrids made by DuPont and other companies. By varying the above factorsin combination with the angles of the lasers, almost any pattern can beprogrammed into the etching in three dimensions into the dies orcylinders. Again, after the exposures are made, protected metal orpolymer left remains in place while the remainder of unprotectedsurfaces/material is removed such as with acid or the like depending onthe material of the die or roller surface. One can create microscopicstructures in three dimensions programmed into a data storage filethrough these photo-polymeric exposure methods and lasers that moveaxially or otherwise to expose the selectively protected surface of thedie or cylinder to be used as an embossing tool to form lensmicrostructures.

Another preferred method of forming lens arrays according to the presentinvention is by using an ultraviolet (UV) or e-beam coating to form thestructures in a web over a film or substrate (i.e., the lens array wouldinclude both the substrate and the web/coating in its array thickness).In a first embodiment of such coating processes, a base film is usedthat may be any of the films mentioned above. The film may be coatedwith a UV coating at about 1 to 5 mils, and the coating can be curedthrough an engraved roller which may be glass or clear plastic. Theroller is clear such that the UV or E-beam is directed to pass throughthe roller while it is in contact with the substrate and squeezing thecoating into place on the base film, whereby the microstructures areformed exactly or within very tight tolerances while they are cured toform a lens array as shown in the included figures.

There are other preferred or alternative methods of using e-beam curingor UV curing to make lens arrays with lens microstructures rather thanusing a clear cylinder to shine UV light through while in contact withthe embossing cylinder. For example, one coating method uses a modifiedlaminator to emboss the pattern onto one surface of a film or substrate.This can be done or accomplished with very little pressure using anengraved cylinder and an application roller that applies UV or e-beamcoating to the film (which is likely to be propylene, PET, or the like).The coating on the film or substrate is then cured through the filmwhile the film is in contact with the embossed roller. In this method,the speed can be in excess of 10,000 feet per hour and can be donewithout excessive wear on the embossing cylinder. A downside or possibleissue with this method is the cost, which tends to be higher because ofthe UV liquid used to cast the impression. However, because most of thelens microstructures are less than a few microns deep, a thin coating issufficient for producing the lens microstructures (e.g., a coating ofless than about 1 mil and more typically less than about 0.3 mils suchas about 0.25 mils may be used successfully to create a plurality oflens sets or microstructures with a coating).

In an alternative coating process, a base film is coated with any of theclear coatings mentioned above (keeping in mind that any coating and itsrefractive index is combined with the thickness and appropriate filmrefractive index for the appropriate and pre-engineered thickness of thelens array). After the coating is applied to the substrate, it is curedand then embossed. In some cases, the coating is only partially curedand then embossed while it is in a semi-liquid state. In some othercases, the coating on the substrate or base film is embossed in a totalliquid state or more liquid state and then cured after the embossingsuch as down the web a few feet up to several hundred feet. In theformer case where the liquid is partially cured, the coating may have afinal curing later down the production line either immediately or downthe web several feet, and in some cases, the coating may bepre-engineered to post cure in a solid state several hours or even dayslater to an acceptable hardness.

As shown in FIGS. 1-12, the display assemblies of the present inventiongenerally include a lens array combined with an interlaced image. Thelens array and the interlaced image may be combined into an assembly orproduct in numerous ways to practice the invention. For example,printing of the interlaced image can occur first in gravure,flexography, offset (lithography), screen-printing, or digitally priorto the application of the micro lens structures (e.g., before a lensarray and interlaced image are combined). This printing could appear inroll, sheet fed, or other method in any of the printing methods. Afterthe interlaced graphic is printed, the lens array or film havingnumerous lens sets or lens microstructures on one side is applied to theinterlaced image (or a substrate upon which the image is printed) byfilm lamination of a pre-embossed lens structure. This application offilm to the pre-printed roll or sheet fed structure can be done in lineon a web press (gravure, flexo, web offset, or any other press feedingroll stock) either in line with the printing or off line in a postlamination process.

In some embodiments, the film is applied with a water based adhesive,hot melt, or thermal adhesive such as is extruded in EVA or othermethods directly onto the film with a hot melt polymer such aspolyethylene, common to the thermal lamination area. Any adhesive usedpreferably is as clear as possible, and its refractive index is takeninto account in the total calculation of each of the polymers and thethicknesses and combined appropriately to equal the correct combinedrefractive index necessary to focus the lens microstructures on thepre-interlaced images. The necessary “critical” alignment is as setforth in the attached figures, so that the interlaced printed image andthe lens structures coincide properly and align along their elongateaxes as shown. This process can be done in line with the printing in aweb or roll format or off-line later after the roll is printed. Again,the adhesive is preferably clear and the thickness of the adhesive andits refractive index is known so that the total of the polymers (orsubstrate layers of a finished product) has a desired refractive indexto focus to the interlaced images underneath the combined layers orsubstrates (e.g., underneath the lens microstructures in the lens array,an adhesive layer, any primer layers, and any other material thicknessesbetween the lens' surfaces and the interlaced image slices).

The combination of the lens array with the interlaced image may also bedone in sheet form, such as with the printed sheet or cardboard in aninterlaced form and then post laminated with a pre-embossed (and manytimes pre-adhesive) coated substrate or film roll containing the lensmicrostructures for displaying the interlaced images. Again, thealignment in the proper direction is important. The display assemblyfabrication can be done with a Bellhofer, D and K Laminator, GBClaminator or other types of laminators that apply film through hot melt(EVA type, extruded, and activated between 180° F. and 350° F.) orsolvent-based pressure sensitive, urethane, or water based adhesive.Again, line up or Y-axis registering is important to achieve desiredresults. Normally, in a sheet fed environment for packaging, the sheetsof paper or plastic would be printed with an interlaced image. Then, theroll of pre-embossed film (or roll of lens array material) would beattached through whatever adhesive process is being used such as heatpressure, or a combination of both.

Much as described above, UV, E-beam, water-based embossed, and otherpost-print coatings may be applied directly to the printed substrates.For example, these coatings that provide the lens array may be appliedvia application roller in the appropriate and pre-engineered thicknessfor the correct combination of refractive indexes to form the lensmicrostructures on top of or adjacent to the printed interlaced image onthe substrate (e.g., plastic, paper, or other material substrates orlayers). The coatings may be embossed over the interlaced printing byway of an engraved cylinder, flat die, or other method using pressure orheat and pressure thereby forming the coating into a lens array of manylens sets or lens microstructures. The coating may also be partiallycured before embossing, uncured in liquid state, or partially cured andpost-cured later by means of E-beam, UV, or any other method includingsolvent or water evacuation. This embossing may be in the form of a rollor sheet and will be accurately post embossed.

In some embodiments, it is desirable to use printing offset, digitalprinting, screen printing, or other printing onto a sheet fed film orweb and then to apply a lens array. For example, a film may be embossedto contain the lens array (e.g., a plurality of lens sets or lensmicrostructures) and then be laminated to the preprinted substrate inline or in an off line process. The interlaced image is printed so thatthe files match the lens array configuration and its lens sets exactlyor within tight tolerances, with such alignment generally being requiredto be excellent as with any lens system to achieve desirable results.The film upon which the lens array is embossed can have an EVA adhesiveupon the non-lens or planar side and be applied with a Bellhofer, D andK or other thermal laminator at about 150 feet per minute over thesubstrate. This is particularly advantageous for printing cartons andthicker boxes. The substrate, e.g., cardboard or board of some type suchas SBS and boards of 10 mils to over 40 mils, can be printed with theinterlaced image on a traditional sheet fed system such as a Heidelberg,Komori, Roland, KBA, and the like. The interlaced image can berelatively coarse (such as 20 to 60 LPI), and the microstructuresapplied can be embossed on the film, which will total up to about 2 toabout 10 mils or more in thickness. The lens array (e.g., the embossedfilm combined with any adhesive/primer) functions similarly to andprovides the quality that a conventional lenticular lens array over 80mils thick would provide. Obviously, not only is it impractical to use alens over 80 mils, it is also cost prohibitive for most applications. Incontrast, the embossed film of the present invention costs very littleto produce and packaging an item or product with that lens array (e.g.,a wrap or the like) will have a dramatic effect (e.g., in someembodiments over 40 views of animation are provided with only a few milsof lens array material).

Any and all of the methods described herein can be re-produced using acombination substrate with the same results and methods of manufacture.In these embodiments, the substrate or film itself can be made inseveral different ways. The base films maybe a combination of APET,PETG, and/or combinations of film such as PET and other softer films. Inmany cases, the top line or layer of film is a softer film likepolyethylene combined with a tougher substrate such as a polypropylene.In these combination substrates used for forming lens arrays, the basefilm can provide stability while the top film can be softer and easierto emboss with the lens sets or lens microstructures of the presentinvention to form a lens array including the top film and toughersubstrate. An ideal combination may be a PET base film with a softerpropylene film laminated with a solvent based adhesive or solvent lessadhesive such as a urethane adhesive like “More Free 403” by Rohm andHaas. The top film can be laminated with a thermal film EVA adhesive aswell.

As described with reference to FIG. 1 and elsewhere, a display assemblycan readily be formed simply by printing directly on the reverse side ofa pre-embossed film or substrate (i.e., onto the back or planar surfaceof a lens array). One efficient method of production of displayassemblies involves printing onto a pre-embossed film a pre-engineerednumber of interlaced image slices or sets of slices, e.g., sets ofslices equal in number to the number of lens microstructures in the lensarray opposite the interlaced image. The printing can occur in sheet orroll form at a very high rate of speed (e.g., over 2,000 feet perminute). The film may be printed in a course and easy to printinterlaced image configured for a conventional lenticular material of 20LPI or less. Most of the lens sets created at this frequency are aspowerful for imaging as the normal thicker counterpart found inconventional lenticular material. In this case, the film lens will be asmuch as 98% thinner and more cost effective to show animation and 3D.One benefit is that the display assemblies or products formed to includea lens array of the present invention with a corresponding or matchedinterlaced image can be produced for about the same cost as a normalfilm laminated product that is not configured for displaying interlacedimages. With implementation of the present invention, it is anticipatedthat it will become acceptable to print to the back of the lens with thecorrect file and application. This is significant when it is comparedwith the manufacture of conventional lenticular material device becausethe invention allows one to print in web, which would be impossible withthe thicker conventional lenticular material. In contrast, an equivalentconventional lens may be more than 100 mils thick and could not even beprinted offset. Costs are expected to be extremely low and representless than 5% (i.e., a 95% cost savings) of traditional lenticularmaterials, and further, traditional lenticular material cannot beprinted in web.

Although the invention has been described and illustrated with a certaindegree of particularity, it is understood that the present disclosurehas been made only by way of example, and that numerous changes in thecombination and arrangement of parts can be resorted to by those skilledin the art without departing from the spirit and scope of the invention,as hereinafter claimed. The above discussion provided examples of lenssets with linear or elongated lenses. However, in some embodiments, theteaching of the lens microstructure or lens sets each configured toprovide focusing on one or more interlaces (i.e., a subset) of a segmentset can be applied to produce non-linear lens sets. For example, thelens sets may be alternative shapes with round (concentric lensesextending out from a round center lens or “bugs eye” arrangements ofround or other-shaped lenses), square, and diamond shaped structuresbeing just a small portion of the possibilities to extend the teachingof lens sets described herein.

The above description mainly provides a description of lens arraysformed from numerous lens microstructures in which an odd number oflenses are provided with a center sublenticule or lens and two mirrorimage side sets of lenses. While this is one preferred configuration formany applications, the center lens or sublenticule need not have exactlyzero degrees of deviation for the rays and lens sets may also have aneven number of sublenticules or lenses. For example, the sublenticuleimmediately to the left of the center of the lens set is, in someembodiments of the invention, designed to deviate the interlace rays −1degree and the sub lenticule immediately to the right of the center ofthe lens set could be designed to deviate the rays +1 degree. The secondlenticule left of the center of the lens set could have a deviationdesign of 3 degrees and so on. A comparison of angular steps ordeviations of two lens sets of the invention, one with a centerlenticule designed for zero degrees as in many examples of the presentdescription, with a similar design with no center lens or sublenticule,is given as follows: −8, −6, −4, −2, 0, 2, 4, 6, 8 for one embodimentand −7, −5, −3, −1, 1, 3, 5, 7. Each of these lens set designs has 2degrees of deviation from sublenticule to sublenticule and would likelyfunction similarly (e.g., be hard to distinguish from one another in usein displaying an interlaced image). The concepts described above for oddnumbered lens sets can easily be extended to such even numbered lenssets, and these “non-zero” designs are, of course, considered within thebreadth of the current description. Further, the above examples of lenssets typically call for a lens set to provide a centered viewing anglefrom a center lens or center line of a lens set. However, alternativeembodiments may use “biased” lens sets in which the angular distributionis not centered. For example, applications might need or be moreeffective with a bias to the angular design such as a lens set with aneven number of lens with an off-center zero deviation of light rays(e.g., a 6-sublenticule lens set may be arranged with deviations of −8,−6, −4, −2, 0, 2 degrees with many other examples being apparent tothose skilled in the art), which may be useful in a package or productthat might viewed from the side.

PROGRAM LISTING FOR LENS MICROSTRUCTURE GENERATION/CONFIGURATION

tol1=0.0001 ′tolerance for completing loop.

′yy1 is starting y value

icount=0

nummissed=0

pitchsub=PitchOverAll/CDbl(NumberSubLenticules)

n=0 ′start at center to get height of endpoints to use as startingpoints for slant walls

-   -   ′each lenticule uses the previous sidewall height as a starting        point.

thicknesstemp=Thickness ′the temporary thickness is initially set to thedesired thickness

′it will be changed if the thickness tolerance is exceeded and theentire calculation will be repeated until the desired thickness is met.

i=0 ′center spline knot of the nth sub lenticule (in this section n=0and the center lenticule is calculated)

X(n, i)=(XLenticuleEnd(n)+XLenticuleEnd(n+1))/2# ′start at center of alenticule

Y(n, i)=thicknesstemp ′go from the center and work out to the ends ofthe lenticule

′left hand side of center lenticule

XDelta=−DelX ′step size of knots.

-   -   While X(n, i)>(XLenticuleEnd(n)+tol1)    -   s1−X(n, i)    -   yy1=Y(n, i)    -   X(n, i)=s1−DelX    -   xx=X(n, i)        ′the values of the y starting position, x position, and step        size to be taken for sublenticule n are passed to a subroutine        which will calculate the y position for the next x location    -   Call YCoOrdinateFind2(n, XDelta, xx, yy1, yy2, Flag)    -   End If    -   If Flag=True Then        -   Y(n, i)=yy2    -   End If

Wend

NumPtsLenLeft(n)=i′ the knot for the left hand side of lenticule n issaved.

′The right hand side of center lenticule is calculated in a similarfashion

*

Etc

*

End If

-   -   NumPtsLenRight(n)=i        ′********************************************

′now do the left side lenticules using the center lenticule end pointsin sidewall sub.

For n=1 To LenNumLeft Step−1

-   -   thicknesstemp=Thickness        GL100:    -   i=0    -   X(n, i)=(XLenticuleEnd(n)+XLenticuleEnd(n+1))/2# ′start at        center of lenticule n    -   Y(n, i)=thicknesstemp ′go from the center and work out to the        ends of the lenticule    -   ′left hand side of lenticule    -   XDelta=−DelX    -   While X(n, i)>(XLenticuleEnd(n)+tol1)        -   s1=X(n, i)        -   yy1=Y(n, i)        -   i=i−1        -   X(n, i)=s1−DelX        -   xx=X(n, i)        -   Call YCoOrdinateFind2(n, XDelta, xx, yy1, yy2, Flag)        -   Y(n, 1)=yy2        -   If Y(n, i)>Thickness Then ′get the adjustment to keep the            thickness uniform            -   If Y(n, i)>thicknessmax Then                -   thicknessmax=Y(n, i)            -   End If        -   End If        -   Else            ′if the case total internal reflection (TIR) was obtained            the slope is calculated in the TIR sub.    -   Call Generate_Lenticule_TIR_End(“Left”, n, i, xx, yy1)    -   nummissed=nummissed+1

End If

Call Generate_Lenticule_Sidewall_Intersect(“Left”, n, i, flagslant)′intersect possibly sloping side wall

Wend

NumPtsLenLeft(n)=i

The right hand side calculation proceeds in a similar manner except forsign change of Xdelta.

′Here is where the resulting maximum thickness is compared to desiredthickness

If (thicknessmax−Thickness)>0.00001*Thickness Then

-   -   thicknesstemp=2#*Thickness−thicknessmax    -   thicknessmax=0#    -   GoTo GL100 ′start over because maximum thickness was larger than        desired

End If

NumPtsLenRight(n)=i

Next n

LenticulesGenerated=True

′for no side walls, start at the center and start each lenticule at theendpoint of the previous lenticule

If SideWalls=“None” Then

XDelta=Del

X(0, 0)=0# ′start at center

s1=−DelX

For n=0 To LenNumRight

-   -   i=0    -   If n=0 And i=0 Then        -   Y(n, i)=Thickness        -   Else        -   Y(n, i)=Y((n−1), NumPtsLenRight(n−1)) ′start the new            lenticule y at the end y of previous lenticule        -   X(n, i)=XLenticuleEnd(n)    -   End If    -   NumPtsLenLeft(n)=i    -   While X(n, i)<(XLenticuleEnd(n+1)−XDelta+tol1)        -   yy1=Y(n, i) ′starting height of element        -   s1=s1+DelX        -   i=i+1        -   X(n, i)=s1+DelX ′x position of next element        -   xx=X(n, i)        -   Call YCoOrdinateFind2(n, XDelta, xx, yy1, yy2, Flag)        -   If Flag=True Then            -   Y(n, i)=yy2            -   Else            -   nummissed=nummissed+1        -   End If    -   Wend    -   NumPtsLenRight(n)=i

Next n

′mirror the center lenticule (only half was done above)

For i=0 To NumPtsLenRight(0)

-   -   j=−i    -   X(0, j)=−X(0, i)    -   Y(0, j)=Y(0, i)

Next i

NumPtsLenLeft(0)=−NumPtsLenRight(0)

′mirror the lenticules (the center is 0 and left alone)

For n=1 To LenNumRight

-   -   k=−n    -   For i=NumPtsLenLeft(n) To NumPtsLenRight(n)        -   j=−i        -   X(k, j)=−X(n, i)        -   Y(k, j)=Y(n, i)    -   Next i    -   NumPtsLenRight(k)=NumPtsLenLeft(n)    -   NumPtsLenLeft(k)=−NumPtsLenRight(n)

Next n

LenticulesGenerated=True

If nummissed>0 Then

-   -   MsgBox (″Number of missed points was ″& nummissed)    -   Exit Sub

End If

End If

End Sub

′the sub that calculates the y position based on the desired raydirection and given x location in the sub lenticule is below

Sub YCoOrdinateFind2(n, XDelta, xx, yy1, yy2, Flag)

′variable declarations are omitted for brevity

Flag=False

′start a course angle step and when the difference is no longerdecreasing, back off and start a smaller

′step size close by. Keep doing this until deltheta reaches a very smallvalue.

xs=XInterlaceCenter(n) ′points for start of ray to be traced

ys=0#

zs=0#

′diff=100000 ′initialize the difference

k=0

halfdelx=XDelta/2#

xint=(xx−halfdelx)

zint=0#

theta=−1.511 ′(radians=−85.6 degrees)

deltheta=0.001

diffmax=100# ′starting point

While deltheta>0.00000000001

k=k+1

theta=theta+deltheta

If Abs(theta)>1.51 Then ′get out of loop, no angle was found to satisfythe ray direction requirement

-   -   Exit Sub

End If

dely=halfdelx*Tan(theta)

yint=(yy1+dely) ′center of line segment under consideration

s1=Sqr((xint−xs)^2+(yint−ys) ^2+(zint−zs) ^2)

c1x=(xint−xs)/s1 ′direction cosines of ray to be traced

e1y=(yint−ys)/s1

e1z=(zint−zs)/s1

xp=xint ′points on the plane perpendicular to line segment

yp=yint

zp=zint

′normal to plane

enx=−Sin(theta)

eny=Cos(theta)

enz=0#

Call intplane(xs, ys, zs, e1x, e1y, e1z, xp, yp, zp, enx, eny, enz, xi,yi, zi, intflag)

If intflag=False Then

-   -   MsgBox (“intplane returned no intersection in Ycoordinate2Find”)

End If

an1=IndexLenticule

an2=IndexAir

Call refract(an1, an2, e1x, e1y, c1z, enx, eny, enz, e2x, e2y, e2z,iflag)

If iflag=3 Then ′(TIR)

-   -   diffmax=100#

End If

If iflag=2 Then ′(refraction)

-   -   s10=e2x−Sin(AngleLenticule(n))    -   diff=Abs(s10)    -   If diff<diffmax Then        -   diffmax=diff        -   Else ′if past minimum, back off and make smaller steps        -   theta=theta−2#*deltheta ′back off angle        -   deltheta=deltheta/3# ′decrease steps        -   diffmax=100# ′get a new starting point    -   End If

End If

Wend

′check limit for slope (needed to prevent tool from clipping sharp pointof sidewall and steepest slope.

If SideWalls=“Hybrid” Then

If Abs(theta)>ThetaSlopeLimitRadians Then

-   -   If theta>=0 Then        -   theta=ThetaSlopeLimitRadians        -   Else        -   theta=−ThetaSlopeLimitRadians    -   End If    -   dely=halfdelx*Tan(theta)

End If

End If

yy2=yy1÷2#*dely

If k<2 Then

MsgBox (″YCoordinatefind K<2 (starting point of yy2 is not smallenough.) xx=“& xx &” yy1−″& yy1)

Exit Sub

End If

Flag True

End Sub

1. A method of fabricating an assembly for displaying an interlacedimage, comprising: providing a film of material that is at leasttranslucent to light; creating a lens array in the film by forming aplurality of parallel lens sets on a first side of the film; and bondingan interlaced image comprising sets of elongate image elements to asecond side of the film; wherein each of the lens set is paired with oneof the sets of the image elements and each of the lens sets comprises aplurality of elongate lenses that are each mapped to a subset of theimage elements in the corresponding paired set of the image elements. 2.The method of claim 1, wherein the mapped subset comprises three orfewer of the image elements.
 3. The method of claim 2, wherein each ofthe lenses of each of the lens sets is configured to focus light fromone of the image elements in the mapped subset.
 4. The method of claim1, wherein each of the lenses in each of the lens sets is configured toprovide a lens-specific viewing angle with a focus line that differsfrom the focus line of the other lenses within the particular lens set.5. The method of claim 4, wherein the lens-specific viewing angles areadditive to provide an overall viewing angle for the lens set.
 6. Themethod of claim 4, wherein each of the lens sets comprises a center lenspositioned centrally in the lens set and further comprises a first setof sides lenses extending from a first edge of the center lens and asecond set of side lenses extending from a second edge of the centerlens, the first set and second set comprising equivalent, even numbersof the side lenses.
 7. The method of claim 6, wherein the lens-specificangles for the center lens and the side lenses in the first and secondsets are equal and selected from the range of about 1 to 10 degrees. 8.The method of claim 6, wherein the number of side lenses in the firstset equals the number of side lenses in the second set, each of the sidelenses in the first set has a cross sectional shape that differs fromthe cross sectional shapes of the other side lenses, and the side lensesof the second set have cross sectional shapes that mirror an oppositeone of the side lenses in the first set.
 9. The method of claim 1,wherein the lens array has a thickness of less than about 15 mils. 10.The method of claim 1, wherein the bonding of the interlaced image to asecond side of the film comprises printing the interlaced image directlyonto the second side.
 11. The method of claim 10, wherein the printingcomprises web printing a rate of at least about 2,000 feet per minuteand wherein the lens array has a thickness in the range of about 1 milto about 5 mils.
 12. The method of claim 1, wherein the bonding of theinterlaced image to a second side of the film comprises bonding with alayer of substantially transparent adhesive interposed between theinterlaced image and the first side of the lens array.
 13. The method ofclaim 12, wherein the adhesive is provided on the second side prior tothe bonding and the bonding comprises thermally laminating the film tothe interlaced image.
 14. The method of claim 1, wherein the creating ofthe lens array comprises embossing the lens sets in the first side ofthe film.
 15. The method of claim 1, wherein the forming of the lenssets comprises coating the first side of the film with a substantiallyclear coating and embossing the coating to contain the lens sets. 16.The method of claim 1, further comprising attaching the bonded lensarray and interlaced image to a packaging surface.
 17. A method ofproducing devices for displaying interlaced images, comprising:providing a sheet of material having an interlaced image on one sidecomprising sets of image slices; providing a film of material that issubstantially transparent to light; embossing a lens array onto a firstside of the film, the lens array comprising lens microstructures; andbonding a second side of the film to the side of the sheet having theinterlaced image, wherein each of the lens microstructures is aligned toone of the sets of image slices.
 18. The method of claim 17, whereineach of the lens microstructures comprises: an elongate center lens witha focus direction; a first set of elongate side lenses extendingparallel to the center lens and abutting a first side of the centerlens, wherein the lenses of the first set each have a unique focusdirection that differs from the focus direction of the center lens; anda second set of elongate side lenses extending parallel to the centerlens and abutting a second side of the center lens, wherein the lensesof the first set each have a unique focus direction that differs fromfocus direction of the center lens.
 19. The method of claim 18, whereinthe lens microstructure has an overall viewing angle comprising acombination of an angular distribution of the center lens, an angulardistribution of each of the lenses of the first set, and an angulardistribution of each of the lenses of the second set.
 20. The method ofclaim 19, wherein the each of the angular distributions is substantiallyequivalent and wherein the angular distributions are selected from therange of about 1 to 10 degrees.
 21. The method of claim 17, wherein thefirst set of side lenses has a cross sectional shape that is a mirrorimage of a cross sectional shape of the second set of side lenses. 22.The method of claim 17, wherein the film has a thickness of less thanabout 15 mils.
 23. The method of claim 17, wherein the lensmicrostructure is configured for focusing on one of the sets of theimage slices and wherein the center lens and each of the lenses in thefirst and second sets focuses on a subset of the image slices.
 24. Themethod of claim 17, wherein the embossing occurs after the bonding ofthe film with the lens array to the sheet having the interlaced images.25. The method of claim 24, wherein the embossing comprises coldembossing including applying pressure to imprint the lens array into thefirst side of the film and using a roller or die comprising a surfacehaving a reverse image of the lens array.
 26. The method of claim 17,wherein the embossing comprises using a chilled roller having a surfacecontoured with a reverse image of the lens array and pressing the firstside of the film after the film is heated to an embossing temperature.27. The method of claim 26, wherein the bonding comprises thermalactivating an adhesive previously applied to the second side of the filmor to the side of the sheet having the interlaced image.
 28. The methodof claim 17, wherein the embossing is performed with a flat die orcylindrical roller that has an embossing surface formed by engravingcomprising photo emulsion with a laser as en exposing light source. 29.A method of forming a device for viewing interlaced images, comprising:providing a sheet with an interlaced image comprising a sets of imageelements, each of the image elements having a predefined width;providing a lens substrate with planar sides; forming a plurality oflens microstructures on one of the planar sides of the lens substrate,each lens microstructure comprising a plurality of lenses; and bondingthe lens substrate to the sheet such that one of the lensmicrostructures is paired with each of the sets of image elements of theinterlaced image such that each of the lenses in each of the setsfocuses light passing through the lens substrate to about the predefinedwidth and onto a paired one of the image elements.
 30. The method ofclaim 29, wherein the cross sectional shape of each of the lenses isselected to focus the light through a plurality of connected segmentshaving differing focus lines onto the paired one of the image elements.31. The method of claim 30, wherein each of the segments is defined by aslope to focus the light onto the paired one of the image elements, eachof the defining slopes is unique for a particular one of the lenses. 32.The method of claim 29, further comprising forming the device by cuttingthe bonded sheet and lens substrate.
 33. The method of claim 32, whereinthe device is selected from the group of products consisting of a label,a decal, a poster, a billboard, a book or magazine cover, a media insertor label, and a card.
 34. The method of claim 29, wherein the forming tothe lens microstructures comprises coating the one of the planar sideswith an ultraviolet (UV) activated coating having a thickness in a rangeof about 1 to about 5 mils, contacting the coating with a cylinderengraved with a mirror image of the plurality of lens microstructures,and curing the coating.
 35. The method of claim 34, wherein the curingis performed concurrently with the contacting by the engraved cylinderby curing the coating with a UV beam directed through the engravedcylinder or through the lens substrate.
 36. The method of claim 29,wherein the forming of the lens microstructures comprises coating theone of the planar sides of the lens substrate with a substantially clearcoating in a non-solid state, embossing the coating to contain theplurality of lens microstructures prior to full curing of the coating toa solid state, and curing the embossed coating to the solid state.